The onset of pregnancy may be associated with hormonal changes leading to the decline in milk yield of buffaloes. To investigate this, forty lactating buffaloes from 1st to 23rd weeks post-conception were selected in a study (Khan et al., 2009). The animals were assigned to three treatments: pregnant with traditional ration, pregnant with supplemented ration, nonpregnant with traditional ration and grouped according to milk yield: HMY, 66 to 75 l/week, n=12; MMY, 56 to 65 l/week, n=16; LMY, 46 to 55 l/week, n=12).

Milk samples (10 ml each) collected from the experimental animals were utilized for composition determination. Milk contents were determined through ultrasonic milk analyzer (model Ekomilk Total Ultrasonic Milk Analyser, Bullteh 2000, Stara Zagora, Bulgharia), using manufacturer's instruction, as already reported (Khan et al., 2007).

Milk progesterone concentrations were measured by enzyme-immunoassay (EIA). Group means were compared and correlation analysis was conducted. Progesterone concentrations increased in almost similar pattern with the advancing weeks post-conception. The high and low yielder showed greater progesterone concentrations in the supplemented than the animals on traditional ration (P<0.001) than the moderate yielders. Progesterone concentrations correlated positively with fat (%), negatively with milk yield, protein (%) and lactose (%) with milk fat content and negatively with protein content and lactose content. The decline in milk yield became drastic when progesterone concentrations rose above 6.44 ng/ml. The pregnant animals on traditional ration exhibited a sharper decline in milk yield with the increasing progesterone concentrations as compared to pregnant animals with supplemented ration. It was concluded that concentrate supplementation induced an increase in progesterone levels. Progesterone concentrations and milk yield showed an inverse relationship.

## **7. Calf suckling and use of oxytocin**

234 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

used to analyze the factors affecting milk yield reduction due to pregnancy:

separately to estimate the effect of pregnancy at different lactation stages.

n=12; MMY, 56 to 65 l/week, n=16; LMY, 46 to 55 l/week, n=12).

greater.

pregnancy was worked out relative to their non-pregnant counterparts. Only the data for lactation weeks after conception were analyzed to find out the milk reduction. Model 3 was

Where Y is milk yield, RY is the reduction in milk yield; L is location, P is parity, LW is lactation week, GM is gestation month, CS is conception season E is the residual term associated with the model. The milk records were divided in three subsets: lactation weeks 11-28 (early lactation); 29-36 (mid lactation); and 37-48 (late lactation) and analyzed

Model 4 was used to modulate milk yield reduction with the onset of pregnancy at medium sized private farms comprising lactation records of 40 buffaloes. The data indicate that postconception reduction in milk yield occurred earliest in those that conceived during 29-36 or 37-48 weeks of lactation, respectively. A noticeable reduction in milk yield was found during the 3rd, 5th or 6th month of pregnancy in the animals conceiving at earlier, mid or later stages of lactation. Initially the milk yield in pregnant animals increased up to 2 months post-conception and then decreased at an almost constant rate. The reduction was visible after 5th week post-conception. The decline in milk with advancing pregnancy was slight up to a point which we declared as joining point; thereafter the decline was much

The onset of pregnancy may be associated with hormonal changes leading to the decline in milk yield of buffaloes. To investigate this, forty lactating buffaloes from 1st to 23rd weeks post-conception were selected in a study (Khan et al., 2009). The animals were assigned to three treatments: pregnant with traditional ration, pregnant with supplemented ration, nonpregnant with traditional ration and grouped according to milk yield: HMY, 66 to 75 l/week,

Milk samples (10 ml each) collected from the experimental animals were utilized for composition determination. Milk contents were determined through ultrasonic milk analyzer (model Ekomilk Total Ultrasonic Milk Analyser, Bullteh 2000, Stara Zagora,

Milk progesterone concentrations were measured by enzyme-immunoassay (EIA). Group means were compared and correlation analysis was conducted. Progesterone concentrations increased in almost similar pattern with the advancing weeks post-conception. The high and low yielder showed greater progesterone concentrations in the supplemented than the animals on traditional ration (P<0.001) than the moderate yielders. Progesterone concentrations correlated positively with fat (%), negatively with milk yield, protein (%) and lactose (%) with milk fat content and negatively with protein content and lactose content.

Bulgharia), using manufacturer's instruction, as already reported (Khan et al., 2007).

Y = L + P + LxP + LW + GM + E (1)

RY = L + CS + P + LW + GM + E (3)

Y = L + P + LxP + LW + E (2)

Calf suckling and oxytocin injections are commonly used for pre-milking stimulus in dairy buffaloes under field conditions. A study was conducted to investigate effect of these treatments on reproductive performance (Qureshi and Ahmad, 2008). We found a lower reproductive efficiency of dairy buffaloes under the peri-urban farming system reflected by ovarian cyclicity in 68.63% buffaloes within 150 days postpartum and silent estrus in 51.5% of the cases. Increasing suckling duration and use of oxytocin extended the postpartum ovulation interval (POI), however it was shortest in buffaloes suckled for one month. Fatcorrected milk (FCM) was signicantly higher in estrus group as compared to anestrus one, during the rst two months postpartum (15.09 versus 13.56 kg/day, P < 0.01). The moderate yielders had shortest postpartum uterine involution (P < 0.01) and estrus intervals (PEI, P < 0.05) and highest conception rate (P < 0.01). It was suggested that the high yielding buffaloes also manifested better reproductive cyclicity.

As the calves were allowed to suckle two times daily, it probably resulted in adverse effect on resumption of postpartum ovarian activity and increased PEI and POI. There was also a decrease in the duration of lochia discharge, which might have been due to sustained uterine contractions caused by oxytocin released in response to suckling. In agreement with this study, ovarian cyclicity was re-established earlier in non-suckled than suckled river, as well as swamp, buffaloes (El-Fouly et al., 1976; El-Fadaly, 1980; Jainudeen et al., 1984). In Nili-Ravi buffaloes, Usmani et al. (1985) reported that postpartum intervals to uterine involution, resumption of follicular development, first rise in milk progesterone, first palpable corpus luteum formation and first oestrus were longer for limited-suckled buffaloes than for non- suckled buffaloes.

For stimulation of milk letdown, oxytocin is released in response to tactile teat stimulation. The application of a fixed pre-stimulation of 30 to 60 s before milking has been recommended to ensure immediate and continuous milk flow after the start of milking (Rasmussen et al., 1992). However, recent investigations demonstrated the importance of the udder fill on the course of milk ejection (Dzidic et al., 2004). Therefore, pre-stimulation time according to the degree of udder fill in individual cows may improve the milking performance. According to previous results, no cisternal milk was available when milking started without prestimulation at a low udder fill (Bruckmaier and Hilger, 2001). At moderate udder fill, cisternal milk was immediately available for milking (Bruckmaier and Blum, 1996) and the alveolar milk ejection started about 70 s after the start of pre-stimulation, as indicated by the second rise of milk flow (Bruckmaier and Hilger, 2001). In full udders, the amount of cisternal milk was further enhanced (Pfeilsticker et al., 1996) and the lag time until the start of the alveolar milk ejection was further reduced (Bruckmaier and Hilger, 2001).

Milk yield in buffalo is lower than cattle because of the little progress made in its conversion to a specialized dairy animal. So the udder is not full and a stronger pre-milking stimulus is required for milk let down. In the present study, representative of the conventional buffalo farming, the suckling (twice a day for five minutes each time) was used or it was replaced by oxytocin in case of death of the calf. Qureshi and Ahmad (2008) suggested that increasing suckling duration and use of oxytocin delayed POI, however, POI was shortest in buffaloes suckled for one month.

## **8. Milk fatty acids**

Buffaloes usually maintain higher body condition and do not produce milk at the cost of their own body reserves under tropical conditions. The mobilization of body reserves for fulfilling the demands of lactation has been extensively studied in dairy cows while limited work is available on this aspect in dairy buffaloes. Therefore, a study was conducted to examine variations in milk fatty acid profiles with body condition in Nili-Ravi buffaloes (Qureshi et al., 2010). We suggested that Nili-Ravi dairy buffaloes produce similar milk to dairy cows regarding content of cardioprotective fatty acids, with the highest concentration of C18:1 cis-9. Two HCFA (hyper-cholesterimic fatty acids, C12:0 and C14:0) were associated with higher body condition. Buffaloes with moderate body condition yielded milk containing healthier fatty acids (the unsaturated fatty acids).

The HCFA (C12:0, C14:0 and C16:0) found in this study on Nili-Ravi buffaloes were considerably lower and cardioprotective fatty acids (C18:1 and C18:2 and C18:3) level were higher than the Bulgharian Murrah buffaloes as reported by Mihaylova and Peeva (2007). They found that total amount of SFAs (saturated fatty acids) were 72.15% (varying from 64.92 to 77.60%), PUFA (poly unsaturated fatty acids) 3.15% and the HCFA were 43.62%. Our values were in close agreement with Fernandes et al. (2007) who reported that the total SFAs, MUFA (mono unsaturated fatty acids) and PUFA in Murrah buffaloes in Brazil were 65.04%, 31.68% and 3.28% respectively and the HCFA varied from 32.48 to 42.90%. Our values for dairy buffaloes were not much different from dairy cows where the SFAs varied from 60 to 65% and UFAs (unsaturatred fatty acids) 35 to 40% of the total fatty acids (Lock and Shinfield, 2004).

Talpur et al. (2008) compared milk fatty acid composition of Nili-Ravi and Kundi buffaloes in Sindh province of Pakistan. The average SFAs were; 66.96 g/100 g and 69.09 g/100 g; MUFA 27.62 and 25.20 g/100 g; PUFA 2.77 and 2.76 g/100 g and HCFA 42.8 and 46.54 g/100 g, of total fatty acids for Kundi and Nili-Ravi breed respectively. It appears that the cardioprotective quality of milk from Nili-Ravi buffaloes is almost similar to dairy cows and Brazilian and higher than in milk from Bulgharian Murrah buffaloes (Talpur et al., 2008).

The opposite pattern of BCS and UFAs concentration in milk fat (Qureshi, et al., 2010) in dairy buffaloes was probably due to lipolysis. In bovine adipose tissue, C18:1 cis-9, C16:0, and C18:0 account for nearly 90% of fatty acids in molar proportions (Christie, 1981) and body fat mobilization would probably increase direct accumulation of these fatty acids into milk fat. In addition, desaturation of stearic acid occurs in the intestinal epithelium and mammary tissues (Enoch et al., 1976). Some 40-50% of C18:1 cis-9 in milk fat is formed from C18:0 in the mammary gland via desaturase (Chilliard et al., 2000). The net outcome of all these processes is the higher level of UFA and more specifically the C18:1 concentration in milk fat.

## **9. Drinking water quality**

236 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

alveolar milk ejection was further reduced (Bruckmaier and Hilger, 2001).

containing healthier fatty acids (the unsaturated fatty acids).

suckled for one month.

**8. Milk fatty acids**

and Shinfield, 2004).

milk was further enhanced (Pfeilsticker et al., 1996) and the lag time until the start of the

Milk yield in buffalo is lower than cattle because of the little progress made in its conversion to a specialized dairy animal. So the udder is not full and a stronger pre-milking stimulus is required for milk let down. In the present study, representative of the conventional buffalo farming, the suckling (twice a day for five minutes each time) was used or it was replaced by oxytocin in case of death of the calf. Qureshi and Ahmad (2008) suggested that increasing suckling duration and use of oxytocin delayed POI, however, POI was shortest in buffaloes

Buffaloes usually maintain higher body condition and do not produce milk at the cost of their own body reserves under tropical conditions. The mobilization of body reserves for fulfilling the demands of lactation has been extensively studied in dairy cows while limited work is available on this aspect in dairy buffaloes. Therefore, a study was conducted to examine variations in milk fatty acid profiles with body condition in Nili-Ravi buffaloes (Qureshi et al., 2010). We suggested that Nili-Ravi dairy buffaloes produce similar milk to dairy cows regarding content of cardioprotective fatty acids, with the highest concentration of C18:1 cis-9. Two HCFA (hyper-cholesterimic fatty acids, C12:0 and C14:0) were associated with higher body condition. Buffaloes with moderate body condition yielded milk

The HCFA (C12:0, C14:0 and C16:0) found in this study on Nili-Ravi buffaloes were considerably lower and cardioprotective fatty acids (C18:1 and C18:2 and C18:3) level were higher than the Bulgharian Murrah buffaloes as reported by Mihaylova and Peeva (2007). They found that total amount of SFAs (saturated fatty acids) were 72.15% (varying from 64.92 to 77.60%), PUFA (poly unsaturated fatty acids) 3.15% and the HCFA were 43.62%. Our values were in close agreement with Fernandes et al. (2007) who reported that the total SFAs, MUFA (mono unsaturated fatty acids) and PUFA in Murrah buffaloes in Brazil were 65.04%, 31.68% and 3.28% respectively and the HCFA varied from 32.48 to 42.90%. Our values for dairy buffaloes were not much different from dairy cows where the SFAs varied from 60 to 65% and UFAs (unsaturatred fatty acids) 35 to 40% of the total fatty acids (Lock

Talpur et al. (2008) compared milk fatty acid composition of Nili-Ravi and Kundi buffaloes in Sindh province of Pakistan. The average SFAs were; 66.96 g/100 g and 69.09 g/100 g; MUFA 27.62 and 25.20 g/100 g; PUFA 2.77 and 2.76 g/100 g and HCFA 42.8 and 46.54 g/100 g, of total fatty acids for Kundi and Nili-Ravi breed respectively. It appears that the cardioprotective quality of milk from Nili-Ravi buffaloes is almost similar to dairy cows and Brazilian and higher than in milk from Bulgharian Murrah buffaloes (Talpur et al., 2008).

The opposite pattern of BCS and UFAs concentration in milk fat (Qureshi, et al., 2010) in dairy buffaloes was probably due to lipolysis. In bovine adipose tissue, C18:1 cis-9, C16:0, The heavy metal content of human diets can adversely affect health status of the consumers. One source of animal feeds include drinking water. Free access to drinking water favorably affected fertility of buffaloes. A study was therefore conducted to investigate the mineral contents of milk (Qureshi and Khan, 2011). The study concluded that the drinking water was the major source of heavy metal contents (Cr, Cd, Pb) in milk produced in the periurban buffalo dairy farms in Peshawar. Peshawar was below the desirable limits of the beneficial inorganic minerals (Mg, Zn and Fe) whereas the toxic heavy metals (Cd, Cr and Pb) content of heavy metals were excessive in drinking water. Levels of the heavy metals Cd, Cr and Pb through milk alone was much more than the total daily intake of these heavy metals from all sources. Free access to drinking water effected milk yield, body condition and fertility favorably. The higher intake of lead was associated with depressed milk in addition to enhanced level of this element in the milk.

The study revealed that drinking water used at urban and peri urban dairy farms in Peshawar are below the maximum allowable intake (MAC) in essential minerals and the heavy metals are higher. The Ca and Mn concentration in drinking water were 63.6% and 40% above the MAC of Pakistan Council of Research on Water Resources (PCRWR). While other essential minerals Mg, Fe, Zn and Cu were 57%, 57%, 99.6% and 98% respectively below the MAC of PCRWR. The heavy metals Cd, Cr and Pb levels were above the MAC of PCRWR (700%, 1800% and 1240% respectively) and were also above the standards fixed for livestock drinking water by NRC (1500%, 850% and 4366.7% respectively). The concentrations of the three heavy metal were far above the standards of WHO (2566.6%, 1800% and 6600%).

Although, food is the major source of mineral nutrients in the diet, drinking water can contribute variable fractions of the total intake (WHO, 2004). The magnesium content of water is variable and depends on the region of its source and its manner of storage. 'Hard' water has a higher concentration of magnesium salts (COMA, 1991). The NIRS (National Inorganic Radionuclide Survey, WHO 2004) study provided data on many cationic inorganic ions in water including calcium and magnesium. They found that mean concentrations (49 mg/L for calcium and 16 mg/L for magnesium) were low compared to their dietary requirements. The 90th percentile values (97 mg/L for calcium and 36 mg/L for magnesium would make more substantial contributions to dietary intake (WHO, 2004). The findings of present study showed a substantial contribution of Ca (327 mg/L) but a low contribution of Mg (24 mg/L) to dietary intake.

Somasundaram et al., (2005) found that technological progress, various industrial activities and increased roadway traffic have caused a signicant increase in environmental contamination. Ubiquitous presence of some metal pollutants, especially cadmium (Cd), chromium (Cr) and lead (Pb), facilitates their entry into the animal food chain and thus increases the possibility of inducing toxic effects in humans and animals. Land application of sewage sludge, sewage water and industrial wastes gradually increases the toxic metals in the soil environment which are increasingly taken by plants and subsequently transferred into the food chain potentially causing severe damage to both animal and human health.

Due to lack of any strict legislation or its implementation for the proper disposal of industrial wastes in Pakistan these wastes become mixed with drinking water channels. In the present study the high level of heavy metals in the drinking water may be due to sewage water contamination and industrial pollution of livestock drinking water and the farmers pay no attention for the provision of clean drinking water to the livestock.

A comparison of the daily intake of minerals and heavy metals through milk to the maximum of allowable intake from all sources was done by the Expert group on vitamins and minerals (2003). Based upon the per capita milk consumption in the country calculated on the basis of Economic Survey (2009-10), the daily intakes of Ca, Mg, Fe, Zn, Cu, Mn, Cd, Cr and Pb through milk were 650.67, 78.27, 32.91, 10.42, 0.50, 0.46, 1.64, 30.84 and 9.27 (mg/day) respectively. The contributions of milk in the maximum daily intake of essential minerals were 14.45% (Ca), 5.5% (Mg), 74.79% (Fe), 13.53% (Zn), 4.54% (Cu) and 3.06% (Mn). The daily intake of toxic heavy metals Cd, Cr and Pb through milk were 1952.38%, 3896% and 1865.19% above the maximum allowable intake of heavy metals from all sources fixed by EVM (Expert Group On Vitamins And Minerals 2003). The milk produced in Peshawar contributes a slight amount of essential minerals to the total daily intake but a considerable amount of toxic heavy metals reflecting poor quality of milk.

In the present study iron significantly (P<0.05) affected milk yield, body condition score and services per conception. Iron in drinking water is probably the most frequent and important contaminant in dairy cattle. Whereas, iron deficiency in adult cattle is very rare because of abundant iron (Fe +3, ferric iron) in feedstuffs, excess total iron intake can be a problem; especially when drinking water contains high iron concentrations. Iron concentrations in drinking water of greater than 0.3 ppm are considered a risk for human health, and are a concern for dairy cattle health and performance. The first concern is that high iron in drinking water may reduce the palatability (acceptability) and therefore amount and rate of water intake. Also, formation of slime in plumbing by iron-loving bacteria may affect water intake and even the rate and volume of water flow through pipes.

The predominant chemical form of iron in drinking water is the ferric (Fe +3) form. The ferrous form is very soluble in water compared with the highly insoluble ferric (Fe) form present in feed sources. Highly soluble iron can interfere with the absorption of copper and zinc. The ferritin system in cells in the intestinal wall normally helps control the risk of iron toxicity in animals by controlling iron absorption. However, highly soluble ferrous iron can be readily absorbed by passing between cells; thus escaping the normal cellular regulation. Once in the body, the transferrin and lactoferrin systems normally bind iron in blood and tissues to control its reactivity. These systems also help control risk of toxicity under normal conditions.

However, when excess, highly water-soluble iron in drinking water is absorbed there is an overload systemically within the animal and all can not be bound. Deleterious consequences of excess free iron include abundant and excessive amounts of reactive oxygen species (e.g., peroxides) that cause oxidative stress. Oxidative stress damages cell membrane structure, functions, and perturbs otherwise normal biochemical reactions. Consequences of iron toxicity and heightened oxidative stress that are magnified in transition and fresh cows include: compromised immune function, increased fresh cow mastitis and metritis, greater incidence of retained fetal membranes as well as diarrhea, sub-normal feed intake, decreased growth, and impaired milk yield. Excess iron (greater than 0.3 ppm) in drinking water is much more absorbable and available than iron from feedstuffs, and thus present a greater risk for causing iron toxicity (Beede 2006).

The number of services per conception (SPC) was increased with increasing Mn, showing its adverse effect. Expert Group on Vitamins and Minerals (2003) reported that manganese has low acute toxicity but has neurotoxic efffects on fertility. Amal (2003) concluded that long exposure of animals to lead affect the reproductive efficiency in the form of lower conception rates, as well as increased incidence of still births, SPC and abortions. The mothers exposed to Pb suffered reduced postnatal viability and lower birth weight.

## **10. Conclusion**

238 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

pay no attention for the provision of clean drinking water to the livestock.

amount of toxic heavy metals reflecting poor quality of milk.

intake and even the rate and volume of water flow through pipes.

Somasundaram et al., (2005) found that technological progress, various industrial activities and increased roadway traffic have caused a signicant increase in environmental contamination. Ubiquitous presence of some metal pollutants, especially cadmium (Cd), chromium (Cr) and lead (Pb), facilitates their entry into the animal food chain and thus increases the possibility of inducing toxic effects in humans and animals. Land application of sewage sludge, sewage water and industrial wastes gradually increases the toxic metals in the soil environment which are increasingly taken by plants and subsequently transferred into the food chain potentially causing severe damage to both animal and human health.

Due to lack of any strict legislation or its implementation for the proper disposal of industrial wastes in Pakistan these wastes become mixed with drinking water channels. In the present study the high level of heavy metals in the drinking water may be due to sewage water contamination and industrial pollution of livestock drinking water and the farmers

A comparison of the daily intake of minerals and heavy metals through milk to the maximum of allowable intake from all sources was done by the Expert group on vitamins and minerals (2003). Based upon the per capita milk consumption in the country calculated on the basis of Economic Survey (2009-10), the daily intakes of Ca, Mg, Fe, Zn, Cu, Mn, Cd, Cr and Pb through milk were 650.67, 78.27, 32.91, 10.42, 0.50, 0.46, 1.64, 30.84 and 9.27 (mg/day) respectively. The contributions of milk in the maximum daily intake of essential minerals were 14.45% (Ca), 5.5% (Mg), 74.79% (Fe), 13.53% (Zn), 4.54% (Cu) and 3.06% (Mn). The daily intake of toxic heavy metals Cd, Cr and Pb through milk were 1952.38%, 3896% and 1865.19% above the maximum allowable intake of heavy metals from all sources fixed by EVM (Expert Group On Vitamins And Minerals 2003). The milk produced in Peshawar contributes a slight amount of essential minerals to the total daily intake but a considerable

In the present study iron significantly (P<0.05) affected milk yield, body condition score and services per conception. Iron in drinking water is probably the most frequent and important contaminant in dairy cattle. Whereas, iron deficiency in adult cattle is very rare because of abundant iron (Fe +3, ferric iron) in feedstuffs, excess total iron intake can be a problem; especially when drinking water contains high iron concentrations. Iron concentrations in drinking water of greater than 0.3 ppm are considered a risk for human health, and are a concern for dairy cattle health and performance. The first concern is that high iron in drinking water may reduce the palatability (acceptability) and therefore amount and rate of water intake. Also, formation of slime in plumbing by iron-loving bacteria may affect water

The predominant chemical form of iron in drinking water is the ferric (Fe +3) form. The ferrous form is very soluble in water compared with the highly insoluble ferric (Fe) form present in feed sources. Highly soluble iron can interfere with the absorption of copper and zinc. The ferritin system in cells in the intestinal wall normally helps control the risk of iron toxicity in animals by controlling iron absorption. However, highly soluble ferrous iron can be readily absorbed by passing between cells; thus escaping the normal cellular regulation. Based upon the above review it may be concluded that buffaloes kept under the peri-urban dairy farming in Pakistan face huge challenges of survival due to poor physiological support to productivity and low socio-economic status of the farmers resulting in poor management. The breeding efficiency of buffaloes has been reported to show a persistent downward trend (78.20 to 71.38%) during the last decade which may have occurred due to the effects of inbreeding or a deteriorating management conditions at these farms.

Buffaloes show a seasonal breeding with lower milk progesterone levels and higher rates of silent ovulation during spring and summer. The breeding season commences during autumn with lowering intake of crude protein and increasing intake of metabolizable energy. Calcium and zinc intake is higher and phosphorus, copper and magnesium intake is lower during autumn. The onset of breeding season was found to be associated with increasing intake of metabolizable energy and decreasing intake of crude protein. Postconception decline has been associated with onset of pregnancy and rising levels of milk progesterone beyond certain levels. However, the decline may be combated through feed supplementation. The traditional use of oxytocin was found to decrease reproductive efficiency of dairy buffaloes under the peri-urban farming system reflected by ovarian cyclicity in 68.63% buffaloes within 150 days postpartum and silent estrus in 51.5% of the cases. Increasing suckling duration and use of oxytocin extended the postpartum ovulation interval (POI), however it was shortest in buffaloes suckled for one month.

Nili-Ravi dairy buffaloes produce similar milk to dairy cows regarding content of cardioprotective fatty acids, with the highest concentration of C18:1 cis-9. Buffaloes with moderate body condition yielded milk containing healthier fatty acids (the unsaturated fatty acids). Drinking water used at urban and peri urban dairy farms in Peshawar are below the maximum allowable intake (MAC) in essential minerals and the heavy metals are higher. The higher intake of lead was associated with depressed milk in addition to enhanced level of this element in the milk.

## **Author details**

M. Subhan Qureshi *Agricultural Unviersity, Peshawar, Pakistan*

## **11. References**

Dzidic, A., Weiss, D., Bruckmaier, R.M., 2004. Oxytocin release, milk ejection and milking characteristics in a single stall automatic milking system. Livest. Prod. Sci. 86, 61–68.

240 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

of this element in the milk.

*Agricultural Unviersity, Peshawar, Pakistan*

Cairo University, Egypt.

Dairy Res. 63, 201–208.

Zootech. 49:181-205.

(3): 450-453.

filling. J. Dairy Res. 68, 369–376.

Christie). Pergamon Press, Oxford, UK.

management conference las vegas nevada.

Department of Health and Social, Security, London.

**Author details**

M. Subhan Qureshi

**11. References**

Nili-Ravi dairy buffaloes produce similar milk to dairy cows regarding content of cardioprotective fatty acids, with the highest concentration of C18:1 cis-9. Buffaloes with moderate body condition yielded milk containing healthier fatty acids (the unsaturated fatty acids). Drinking water used at urban and peri urban dairy farms in Peshawar are below the maximum allowable intake (MAC) in essential minerals and the heavy metals are higher. The higher intake of lead was associated with depressed milk in addition to enhanced level

Amal, RAH, 2003. Clinicopathological studies on the effect of chronic exposure to lead on different reproductive phases in female baladi goats. Ph. D. Vet. Sci, Fac. Vet. Med.

Bashir, M. K., M. S. Khan, S. A. Bhatti and A. Iqbal. 2007. Lifetime performance of Nili-Ravi

Bhalaru, S. S., M. S. Tiwana and N. Singh. 1987. Effect of body condition at calving, on subsequent reproductive performance in buffaloes. Indian J. Anim. Sci. 57:33-36. Bruckmaier, R.M., Blum, J.W., 1996. Simultaneous recording of oxytocin release, milk ejection and milk flow during milking of dairy cows with and without prestimulation. J.

Bruckmaier, R.M., Hilger, M., 2001. Milk ejection in dairy cows at different degrees of udder

Chillard, Y., A. Ferlay, R. M. Mansbridge and M. Doreau. 2000. Ruminant milk fat plasticity: nutritional control of saturated, polyunsaturated, trans and conjugated fatty acids. Ann.

Christie, W. W. 1981. The composition, structure and function of lipids in the tissues of ruminant animals. Pages 95-191 in Lipid Metabolism in Ruminant Animals (Ed. W. W.

COMA 1991. Report on Dietary Reference Values for Food Energy and Nutrients for the United Kingdom; Committee on Medical Aspects of Food Policy (COMA).

Beede, D.K, 1993. Water Nutrition And Quality For Dairy Cattle. Western large herd

DeRouen, S. M., D. E. Franke, D. G. Morrison, W. E. Yatt, D. F.Coombs, T. W. White, P. E. Humes and B. B. Greene. 1994.Prepartum body condition and weight influences on

Drost, A., 2007. Advanced reproductive technology in the water buffalo. Theriogenology, 68

reproductive performance of first-calf beef cows. J. Anim. Sci. 72:1119-1125.

buffaloes in Pakistan. Asian-Aust. J. Anim. Sci. 20(5):661-668.

	- Qureshi M.S., 2000. Productivity problems in livestock in NWFP and their sustainable solutions. *J. Rural Dev. Admin.,* 32 (2): 73-81.
	- Qureshi, M.S. and R. Khan, 2011. Heavy metals in drinking water of dairy buffaloes. VDM Verlag, Germany.
	- Qureshi, M.S., 1995. Conventional buffalo farming system in NWFP Pakistan. *Buffalo Bull.,* 14: (2) 38-31. (ISSN 0125-6726). Int. Buffalo Inf. Center, Bangkok.
	- Qureshi, M.S., 2008. Dairy Farms and farmers. Social norms and training needs. Pak J Agric Sci,45 (2):215-217.
	- Qureshi, M.S., G. Habib, H.A. Samad, M.M. Siddiqui, N.Ahmad and M. Syed, 2002. Reproduction-nutrition relationship in dairy buffaloes. I. Effect of intake of protein, energy and blood metabolites levels. *Asian-Aust. .J.Anim.Sci*, 15(3): 330-339.
	- Qureshi, M.S., N.Ahmad 2008. Interaction among calf suckling, use of oxytocin, milk production and reproduction in dairy buffaloes. Animal Reproduction Science, 106: 380-392.
	- Qureshi, M.S., S. Khan and N. Ahmad, 2007. Pregnancy depresses milk yield in dairy buffaloes. *Ital. J. Anim. Sci.*, 6 (Suppl. 2): 1290-1293.
	- Qureshi, M.S.; H.A. Samad, G. Habib., R.H. Usmani and M.M. Siddiqui, 1999. Study on factors leading to seasonality of reproduction in dairy buffaloes. I. Nutritional factors. *Asian-Aust. J. Anim. Sci*, 12 (7): 1019-1024.
	- Qureshi, MS, A Mushtaq, S Khan, G Habib, ZA Swati, 2010. Variation in milk fatty acids composition with body condition in dairy buffaloes *(Bubalus bubalis). Asian Aust J Anim Sci,* 23: 340-345.
	- Rasmussen, M.D., Frimer, E.S., Galton, D.M., 1992. The influence of pre-milking teat preparation and attachment delay on milk-yield and milking. J. Dairy Sci. 75, 2131– 2141.
	- Sohail, S.M., M.S. Qureshi, S Khan, G Habib, 2009. Relationship among various production and reproduction Contributors of Breeding Efficiency in Dairy Buffaloes of Pakistan. . *Pak J Zool*., Sup. No.9, 297-301.
	- Somasundaram, J, R. Krishnasamy, P Savithri. 2005. Biotransfer of heavy metals in Jersey cows. Indian J Ani Sci 75:1257–1260.
	- Talpur, F. N., M. I. Bhangera, A. A. Khooharob and G. Zuhra Memon. 2008. Seasonal variation in fatty acid composition of milk from ruminants reared under the traditional feeding system of Sindh, Pakistan. Livest. Sci. 118:166-172.
	- Usmani, R.H., Ahmad, A., Inskeep, E.K., Dailey, R.A., Levis, P.E., Lewis, G.S., 1985. Uterine involution and postpartum ovarian activity in Nili-Ravi buffaloes. Theriogenology 24, 435–448.
	- WHO, 2004. Rolling revision of World health organization guideline for drinking water quality, George Hallberg, USA.
	- Wynn, P., D Harris, R Moss, B Clem, R Sutton and P Doyle, 2006. Report On Dairy Mission To Pakistan. Mission carried out under the auspices of the Australia-Pakistan Agriculture Sector Linkages Program. Government of Punjab, Lahore.

## **Determination of the Herd Size**

Rocky R.J. Akarro

242 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

14: (2) 38-31. (ISSN 0125-6726). Int. Buffalo Inf. Center, Bangkok.

solutions. *J. Rural Dev. Admin.,* 32 (2): 73-81.

buffaloes. *Ital. J. Anim. Sci.*, 6 (Suppl. 2): 1290-1293.

*Asian-Aust. J. Anim. Sci*, 12 (7): 1019-1024.

*Pak J Zool*., Sup. No.9, 297-301.

quality, George Hallberg, USA.

cows. Indian J Ani Sci 75:1257–1260.

feeding system of Sindh, Pakistan. Livest. Sci. 118:166-172.

Verlag, Germany.

Sci,45 (2):215-217.

380-392.

*Sci,* 23: 340-345.

2141.

435–448.

Qureshi M.S., 2000. Productivity problems in livestock in NWFP and their sustainable

Qureshi, M.S. and R. Khan, 2011. Heavy metals in drinking water of dairy buffaloes. VDM

Qureshi, M.S., 1995. Conventional buffalo farming system in NWFP Pakistan. *Buffalo Bull.,*

Qureshi, M.S., 2008. Dairy Farms and farmers. Social norms and training needs. Pak J Agric

Qureshi, M.S., G. Habib, H.A. Samad, M.M. Siddiqui, N.Ahmad and M. Syed, 2002. Reproduction-nutrition relationship in dairy buffaloes. I. Effect of intake of protein,

Qureshi, M.S., N.Ahmad 2008. Interaction among calf suckling, use of oxytocin, milk production and reproduction in dairy buffaloes. Animal Reproduction Science, 106:

Qureshi, M.S., S. Khan and N. Ahmad, 2007. Pregnancy depresses milk yield in dairy

Qureshi, M.S.; H.A. Samad, G. Habib., R.H. Usmani and M.M. Siddiqui, 1999. Study on factors leading to seasonality of reproduction in dairy buffaloes. I. Nutritional factors.

Qureshi, MS, A Mushtaq, S Khan, G Habib, ZA Swati, 2010. Variation in milk fatty acids composition with body condition in dairy buffaloes *(Bubalus bubalis). Asian Aust J Anim*

Rasmussen, M.D., Frimer, E.S., Galton, D.M., 1992. The influence of pre-milking teat preparation and attachment delay on milk-yield and milking. J. Dairy Sci. 75, 2131–

Sohail, S.M., M.S. Qureshi, S Khan, G Habib, 2009. Relationship among various production and reproduction Contributors of Breeding Efficiency in Dairy Buffaloes of Pakistan. .

Somasundaram, J, R. Krishnasamy, P Savithri. 2005. Biotransfer of heavy metals in Jersey

Talpur, F. N., M. I. Bhangera, A. A. Khooharob and G. Zuhra Memon. 2008. Seasonal variation in fatty acid composition of milk from ruminants reared under the traditional

Usmani, R.H., Ahmad, A., Inskeep, E.K., Dailey, R.A., Levis, P.E., Lewis, G.S., 1985. Uterine involution and postpartum ovarian activity in Nili-Ravi buffaloes. Theriogenology 24,

WHO, 2004. Rolling revision of World health organization guideline for drinking water

Wynn, P., D Harris, R Moss, B Clem, R Sutton and P Doyle, 2006. Report On Dairy Mission To Pakistan. Mission carried out under the auspices of the Australia-Pakistan

Agriculture Sector Linkages Program. Government of Punjab, Lahore.

energy and blood metabolites levels. *Asian-Aust. .J.Anim.Sci*, 15(3): 330-339.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/28430

## **1. Introduction**

Scientists can work out breeds to be kept for greatest milk yield. Such breeds can differ from area to area and breed to breed. Akarro (1995; 2009) developed a simulation model to identify breeds to be bred for greatest milk yield in selected well managed farms in Tanzania. Having found out the breed to keep for the greatest milk yield, the problem that follows is to work out the herd size or the stocking rate for a particular farm. Also a stocking rate should render a profitability to the farm, otherwise there is no need of carrying out the enterprise of keeping cows. Indeed a simulation model of the form presented in Fig 1 can be used, but the problem is that most of the animal activities can not be quantified neither can they be approximated by the well known probability distributions. Furthermore, even for the approximation of distribution of animal activities, there is a problem of quantifying certain parameters on the quality and quantity of forage on offer and feeds in general. In view of this, a linear programming model can be developed as a proxy to determine the herd size or the stocking rate so that an enlightenment on ways to organize the farm for a profitable farm operation can be achieved. This is done for one farm only which is believed to have the necessary data input for the development of the linear model. The farm selected is Uyole. This method can be adapted to similar farms in the world which operate on the basis of 'zero' grazing.

Zero grazing is hereby defined as

## **1.1. The Uyole Agricultural Centre (UAC)**

The Uyole Agricultural Centre (UAC) is of particular importance in this respect. The predominant dairy breed at Uyole is the Friesian / Zebu cross. Natural pastures around Uyole have been observed to produce around 2500 kg. dry matter (DM/ha/year). Considering a 400 kg cow requiring 8.5 kg. DM/day, then this cow needs 3100 kg DM/year. One hectare cannot therefore, maintain such a cow ( Kifaro & Akarro, 1987). It was therefore

© 2012 Akarro, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Akarro, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

decided that in agricultural high potential areas of Rungwe district (this is the area surrounding Uyole) more productive pasture species were required. Sensing this, the Uyole Agricultural Centre established a pasture and forage research programme. It commenced its work in 1970 with the aim to improve the phytomass and quality of pastures. Initial work involved fertilization of natural pastures, introductions and testing of grass/legume mixtures, special purpose pastures and short term crops like oats, lupine, maize, and fodder sugar beets.

## **2. The Linear Programming (L.P.) model**

Simulation of the cow activities and feeding regimes as shown in Fig. 1 would probably be a more appropriate method for establishing the stocking rate.

However, given the intricacies of implementing this simulation especially with reference to management policies of a particular farm, a linear programming (L.P.) method is suggested as a plausible alternative. Here L.P. is defined as a mathematical structure, involving particular mathematical assumptions that can be solved using a standard solution technique, called the *simplex method.* It is the purpose of this section to formulate a mathematical model that would enlighten us on the type of pastures to be grown, when and what supplementation level is required and the number of dairy animals to keep for the farm to be profitable. It was assumed that a known section of the farm was to be developed entirely to dairy enterprise and the problem was to find how to organize this farm so that its annual net profit would be maximized. An L.P. is suggested. The herd size was kept constant throughout the year. In formulating the L.P. there arose a need of identifying major constraints to dairy cow needs as discussed below.

#### **2.1. Nutritional (energy, protein, minerals and vitamins) requirements of a cow**

#### *2.1.1. Energy requirements*

Organic nutrients obtained from different sources of feed available to an animal are used for a variety of purposes, including maintenance of body functions, the construction of body tissues, the synthesis of milk, and the conversion to mechanical energy used for walking and other work. All these diverse functions require the transfer of considerable quantities of energy, so that in most situations when the energy requirement of the animals' different needs are met, it may be assumed that animal's non-energy requirements (protein-minerals and vitamins) are also met. Hence, the nutritive value of different feeds can be expressed by their energy content or by their ability to supply energy with high coefficient of conversion into usable energy for the different body functions. The gross energy contents of different forages are very similar at about 18 MJ/kg (Hunt, 1966). A portion of this energy is lost as faeces while the remaining digestible energy (DE) proportional to the digestibility (d) of the consumed feed is converted into metabolized energy (ME) after additional losses of about 19% of DE as urine and methane (Armstrong, 1964; MAFF, 1975).

**2. The Linear Programming (L.P.) model**

constraints to dairy cow needs as discussed below.

19% of DE as urine and methane (Armstrong, 1964; MAFF, 1975).

*2.1.1. Energy requirements*

more appropriate method for establishing the stocking rate.

sugar beets.

decided that in agricultural high potential areas of Rungwe district (this is the area surrounding Uyole) more productive pasture species were required. Sensing this, the Uyole Agricultural Centre established a pasture and forage research programme. It commenced its work in 1970 with the aim to improve the phytomass and quality of pastures. Initial work involved fertilization of natural pastures, introductions and testing of grass/legume mixtures, special purpose pastures and short term crops like oats, lupine, maize, and fodder

Simulation of the cow activities and feeding regimes as shown in Fig. 1 would probably be a

However, given the intricacies of implementing this simulation especially with reference to management policies of a particular farm, a linear programming (L.P.) method is suggested as a plausible alternative. Here L.P. is defined as a mathematical structure, involving particular mathematical assumptions that can be solved using a standard solution technique, called the *simplex method.* It is the purpose of this section to formulate a mathematical model that would enlighten us on the type of pastures to be grown, when and what supplementation level is required and the number of dairy animals to keep for the farm to be profitable. It was assumed that a known section of the farm was to be developed entirely to dairy enterprise and the problem was to find how to organize this farm so that its annual net profit would be maximized. An L.P. is suggested. The herd size was kept constant throughout the year. In formulating the L.P. there arose a need of identifying major

**2.1. Nutritional (energy, protein, minerals and vitamins) requirements of a cow**

Organic nutrients obtained from different sources of feed available to an animal are used for a variety of purposes, including maintenance of body functions, the construction of body tissues, the synthesis of milk, and the conversion to mechanical energy used for walking and other work. All these diverse functions require the transfer of considerable quantities of energy, so that in most situations when the energy requirement of the animals' different needs are met, it may be assumed that animal's non-energy requirements (protein-minerals and vitamins) are also met. Hence, the nutritive value of different feeds can be expressed by their energy content or by their ability to supply energy with high coefficient of conversion into usable energy for the different body functions. The gross energy contents of different forages are very similar at about 18 MJ/kg (Hunt, 1966). A portion of this energy is lost as faeces while the remaining digestible energy (DE) proportional to the digestibility (d) of the consumed feed is converted into metabolized energy (ME) after additional losses of about

**Figure 1.** Components of a Dairy Cow Operational System : Source: Modified from Konandreas and Anderson (1982)

#### *2.1.2. Energy requirements for maintenance*

Maintenance can be defined as the state of the animal in which there is neither a net gain nor loss of nutrients (Kay, 1976). Maintenance requirements are estimates of the amount of nutrients required to achieve such an equilibrium. One component of the energy requirements for maintenance is referred to as basal metabolism and is proportional to the body size of the animal. The second component of the energy requirements for maintenance is related to the level of the animals activity and can be expressed approximately by live weight and the daily distance walked. Thus following Blaxter (1969) and Webster (1978), total net energy requirements for maintenance can be obtained from the relationship:

$$E\_m = 0.376 \text{ W}^{T3} + 0.0021 \text{WD} \tag{1}$$

Where Em= net energy requirements for maintenance (MJ/day).

W= live weight (kg)

D= distance walked (km/day).

The efficiency with which metabolizable energy is used for maintenance is a function of metabolizability of the consumed forage (see for example Blaxter, 1974; Van Es, 1976; Ministry of Agriculture Fisheries and Food (MAFF); 1975; Pigden et. al; 1979).

According to MAFF when distance walked is negligible, equation (2.1) reduces to

$$E\_m = 8.3 + 0.091 \text{ W. (MAFF, 1975)} \tag{2}$$

Where Em= net energy requirements for maintenance. = metabolizable energy for maintenance (MJ/day). W= body weight

#### *2.1.3. Energy requirements for lactation*

Net energy requirements for lactation are approximately proportional to the quantity of milk produced ( ILCA, 1978), and this is given by

$$\mathbf{E}\_{\rm L} = \mathbf{e}\_{\rm L} \mathbf{M} \tag{3}$$

Where EL= net energy requirements for lactation (MJ/day). eL= energy content of milk. M= milk yield (kg/day).

The energy content of milk is approximately given by the relationship (MAFF, 1975):

$$\mathbf{e}\_{\mathrm{L}} = \begin{array}{c} \text{0.03886 BF} \ + \text{ 0.0205 SNP} \ - \text{ 0.0236} \end{array} \tag{4}$$

where BF= Butterfat content (g/kg). SNF= solids not fat content (g/kg).

#### *2.1.4. Protein requirements*

246 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

Maintenance can be defined as the state of the animal in which there is neither a net gain nor loss of nutrients (Kay, 1976). Maintenance requirements are estimates of the amount of nutrients required to achieve such an equilibrium. One component of the energy requirements for maintenance is referred to as basal metabolism and is proportional to the body size of the animal. The second component of the energy requirements for maintenance is related to the level of the animals activity and can be expressed approximately by live weight and the daily distance walked. Thus following Blaxter (1969) and Webster (1978), total net energy requirements for maintenance can be obtained

.73

The efficiency with which metabolizable energy is used for maintenance is a function of metabolizability of the consumed forage (see for example Blaxter, 1974; Van Es, 1976;

Net energy requirements for lactation are approximately proportional to the quantity of

The energy content of milk is approximately given by the relationship (MAFF, 1975):

Ministry of Agriculture Fisheries and Food (MAFF); 1975; Pigden et. al; 1979).

According to MAFF when distance walked is negligible, equation (2.1) reduces to

Where Em= net energy requirements for maintenance (MJ/day).

Where Em= net energy requirements for maintenance. = metabolizable energy for maintenance (MJ/day).

mE 0.376 W 0.0021WD (1)

E 8.3 0.091 W. MAFF, 1975 <sup>m</sup> (2)

Le 0.03886 BF 0.0205 SNF 0.0236 (4)

L L E eM (3)

*2.1.2. Energy requirements for maintenance*

from the relationship:

W= live weight (kg)

W= body weight

D= distance walked (km/day).

*2.1.3. Energy requirements for lactation*

 eL= energy content of milk. M= milk yield (kg/day).

where BF= Butterfat content (g/kg). SNF= solids not fat content (g/kg).

milk produced ( ILCA, 1978), and this is given by

Where EL= net energy requirements for lactation (MJ/day).

Protein is an essential nutrient for animals. This nutrient however cannot be synthesized in sufficient quantities by animals to meet their requirements. Fortunately it is synthesized by plants and stored in plant cells. Through this means, a source of protein is provided for use by ruminants. An animal's requirement for protein is based on the protein stored in its body; its products such as milk, eggs, or wool; the products of conception, and the metabolic losses in faeces, endogenous losses in urine and by other losses (hair, skin, hoofs, etc.). To maintain an animal in protein equilibrium, these losses must be off set. The sum of these becomes the protein requirement for that animal. Protein requirements can be determined through nitrogen balance studies. In these studies, healthy adult animals are fed an adequate amount of energy and other nutrients in diets that contain different levels of protein. The minimum protein intake that will support nitrogen equilibrium is the maintenance requirement. The protein requirement for lactation is easily calculated by determining the amount of protein present in the milk and multiplying this by 1.25 (Kearl, 1982). Dairy animals seem to adapt very well to a wide range of protein intakes without any ill effects. The protein contained in milk, however, represents a direct loss of protein by the body and obviously this must be replaced.

#### *2.1.5. Protein requirements for maintenance*

The Digestible Protein (DP) maintenance requirements have been quite well defined. Orskov (1976) stated that the rate of protein deposition by young ruminants is appropriately expressed as the nitrogen retained per unit of energy digested, and that the retention of protein per unit of energy digested increases with the level of feeding and decreases as the animal matures. Balch (1976) suggested that at any given intake of protein, the response of the animal may vary greatly depending on the intake of energy. Poppe & Gabel (1977), after reviewing the literature concerning protein requirements for cattle, cited a DP requirement of 3g per kilogram of live weight W raised to power .75 for maintenance based on a digestible organic matter (DOM) fermentation rate of 60%.

Nehring (1970) suggested a value of 2.57g of DP per kilogram of live weight raised to the power .75 as the maintenance requirement of cattle weighing 400 to 800 kg. Sen et. al; (1978) whose data are used as the feeding standard in India, recommended 2.84g DP per kilogram of W.75 for zebu cross bred cattle and buffaloes.

Additional information is needed to substantiate these results, but on the basis of a wide range of values found in the literature and those suggested as standards to be used in several countries an average value of

$$2.86 \text{g DP per kilogram of } \text{W}^{0.75} \tag{5}$$

Where W is the live weight in kg has been used in estimating the DP maintenance requirement. This is the value used in Kearl (1982) which is also used in the formulation of feed values in food stuffs.

#### *2.1.6. Protein requirement for lactation*

Many studies have been done to determine the amount of Digestible Protein (DP) required to produce one kilogram (kg) of milk. Generally, the recommended amounts of DP per kilogram of milk have been correlated with the fat content of the milk. Nehring (1970) proposed a DP requirement of 50 to 80 g of DP for milk containing butterfat content from 3 to 6 percent. Ranjhan et. al; (1977) suggested 4.17 g of DP per kilogram of milk. Patle & Mudgal (1976) agreed with Ranjham et.al; (1977).. The National Research Council (1971) recommends a DP requirement of 42 to 60 g per kilogram of milk containing 2.5 to 6% fat. The Ministry of Agriculture Fisheries and Food (MAFF, 1979) noted a DP requirement of 48 to 63 g of DP per kilogram of milk containing 3.6 to 4.9% butterfat.

The MAFF (1979) values are the ones used in our estimates because they are regarded as standards in the formulation of feed values.

## *2.1.7. Estimation of nutritive values*

On the average, a Friesian cow or a Friesian cross weighs 450 kg and produces milk whose composition is 3.6 percent butterfat (BF) and 8.6 percent solids not fat (SNF) at UAC (Myoya, 1980). Using results (2.2), (2.3), (2.4), (2.5) and (2.6), energy and protein requirements per dairy cow can be calculated on monthly basis for the available milk yields as shown in Table 2.1. The monthly yield figures were obtained from Uyole Agricultural Centre (UAC).

**Table 1.** Monthly Nutrition Requirements per Dairy Cow

Using equation (2.2), the Metabolizable Energy (ME) requirements for maintenance is 1478 Metabolizable Energy in Megajoules (MEMJ) per month. Using equation (2.4) the energy content eL of milk is 4.94 megajoules (MJ) per kilogram. Using equation (2.3). net energy for lactation EL is obtained. This is column 3 of Table 2.1. Using result (2.5), the Digestible Crude Protein (DCP) for maintenance is 279g per day. The value given by MAFF (1979) is 275g per day for a dairy cow of the same weight. DCP for maintenance required in a month is therefore 8.37 kg.

Using expression (2.6) the DCP allowances for milk production per kg for a Friesian cow with Butter fat percentage (BF%) of 3.6% is 48g (MAFF, 1979).

Column 5 in Table 2.1 is obtained by multiplying 48 by milk yield in kilograms plus DCP for maintenance which is 8.37.

## *2.1.8. Energy and protein supply*

248 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

to 63 g of DP per kilogram of milk containing 3.6 to 4.9% butterfat.

monthly yield figures were obtained from Uyole Agricultural Centre (UAC).

Many studies have been done to determine the amount of Digestible Protein (DP) required to produce one kilogram (kg) of milk. Generally, the recommended amounts of DP per kilogram of milk have been correlated with the fat content of the milk. Nehring (1970) proposed a DP requirement of 50 to 80 g of DP for milk containing butterfat content from 3 to 6 percent. Ranjhan et. al; (1977) suggested 4.17 g of DP per kilogram of milk. Patle & Mudgal (1976) agreed with Ranjham et.al; (1977).. The National Research Council (1971) recommends a DP requirement of 42 to 60 g per kilogram of milk containing 2.5 to 6% fat. The Ministry of Agriculture Fisheries and Food (MAFF, 1979) noted a DP requirement of 48

The MAFF (1979) values are the ones used in our estimates because they are regarded as

On the average, a Friesian cow or a Friesian cross weighs 450 kg and produces milk whose composition is 3.6 percent butterfat (BF) and 8.6 percent solids not fat (SNF) at UAC (Myoya, 1980). Using results (2.2), (2.3), (2.4), (2.5) and (2.6), energy and protein requirements per dairy cow can be calculated on monthly basis for the available milk yields as shown in Table 2.1. The

> Net Energy Lactation MJ/Month

Using equation (2.2), the Metabolizable Energy (ME) requirements for maintenance is 1478 Metabolizable Energy in Megajoules (MEMJ) per month. Using equation (2.4) the energy content eL of milk is 4.94 megajoules (MJ) per kilogram. Using equation (2.3). net energy for lactation EL is obtained. This is column 3 of Table 2.1. Using result (2.5), the Digestible Crude Protein (DCP) for maintenance is 279g per day. The value given by MAFF (1979) is 275g per

November 206 1018 2496 18.26 December 270 1334 2812 21.33 January 316 1561 3039 23.54 February 319 1576 3054 23.68 March 376 1858 3336 26.42 April 343 1695 3173 24.83 May 462 2283 3761 30.55 June 389 1922 3400 27.04 July 355 1754 3232 25.41 August 315 1556 3034 23.49 September 346 1709 3187 24.98 October 407 2011 3489 27.91

Metabolizable Energy Required MJ/Month

Protein Required (DCP Kg per Month)

*2.1.6. Protein requirement for lactation*

standards in the formulation of feed values.

*2.1.7. Estimation of nutritive values*

Month Monthly Yield in Kg

**Table 1.** Monthly Nutrition Requirements per Dairy Cow

The main energy and protein source of dairy cows is obtained from the bulky food eaten by the cow. The bulky foods can either be grown on a farm or be purchased. At Uyole, land is scarce and the nutritive value of natural pastures and DM yield is low. Subsequent research involved evaluation of improved pasture and legume species. These included Rhodes grass (*Chloris gayana)*, Napier grass (*Pennisetum purpureum*) *Desmodium spp*.; Nandi setaria, Lucerne, oats, Lupins etc. fertilizer application, cutting frequencies and grass/legume mixture.

Invariably, fertilizer application improved the quality and quantity of the production of feeds/ha but also the cost of production was increased due to input costs.

#### *2.1.9. Fertilizer efficiency*

An increase in nitrogen application leads to increase in Dry matter yield per hectare as can be seen from Table 2.2. However it is desired not to apply infinite amounts of fertilizer but to apply the amounts that will give the maximum yield (kg DM) per unit of fertilizer applied. Such amount will be termed 'efficient' fertilizer applications. Such quantities will be used in our model for the input costs in pasture/crop production. Efficient fertilizer applications were worked out as yield increase per amount of fertilizer applied. Data for yields and fertilizer applications were obtained from UAC. These are presented in Table 2.2

**Table 2.** Dry Matter Yield (kg/ha) of Rhodes Grass and Nandi setaria under Six levels of Nitrogen (Mean of Three Years): Source: Myoya (1980).

The higher yield in Rhodes grass without nitrogen and with rates up to 120kg N/ha suggest that Rhodes grass requires less nitrogen than Nandi setaria. At higher nitrogen rates, the difference disappears.

## **2.2. Forage supply at UAC**

Due to climatic variations at Uyole, certain types of crops are available only in particular months or periods. During the wet season one expects surplus fodder which is not the case in the dry season. Table 2.3 shows the forage/feed supply sequence of some of the animal food stuffs grown at Uyole during the year.

Key: V Available

X Not available

**Table 3.** Availability of Crops

Hay and silage could also be grown and these can be fed at any time during the year although they are usually fed during the dry season.

Thus, the year could be divided into seven periods, in each of which a different combination of crops or grazing output was available as shown in Table 2.3.

## **2.3. Estimation of Metabolizable Energy (ME) and Digestible Crude Protein (DCP) in feed stuffs**

At UAC only a few feed stuffs have had their ME and DCP estimates done. In this case the figures available from the literature are assumed to be similar for the same feed stuffs where ME and DCP estimates are lacking. These are used because even in the formulation of quantity of food required, the estimates found in the literature, especially MAFF (1979), are used (Kurwijila, 1991). Table 2.4 gives Metabolizable Energy in Megajoules (MEMJ), Crude Protein Percentages and Crude Protein Digestibility Coefficient percentages estimates based on one kilogram of Dry matter (Mbwile, et. al; 1981; Gohl, 1981; Bredon, 1963; MAFF, 1979).

\* Approximated the same as grass moderate digestibility silage.

\*\* Approximated the same as grass with high digestibility.

250 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

March-

Due to climatic variations at Uyole, certain types of crops are available only in particular months or periods. During the wet season one expects surplus fodder which is not the case in the dry season. Table 2.3 shows the forage/feed supply sequence of some of the animal

April May June July-

X1 - Natural pasture V V V X X X X

green feed X V V V V V V

feed X V V V V X V

X7 – Oats green feed X V V V X X V

hay X X X X X V X X9 – Maize silage X V V V V V V

silage X X X X V V V

silage X X X X V V X X13- Oats silage X X X X V X X X14- Lupins silage X X X X V V V

Season

V V V V X X V

V V V V X X V

X V V V V V X

X X X X V V V

X X X X V V V

August

September-

November December

**2.2. Forage supply at UAC**

Crop

X2 - Rhodes grass

Rhodes/Desmodium

X4 – Napier grass

X5 – Lupins green

/Desmodium green

X8 – Rhodes grass

X10 – Rhodes grass

Rhodes/Desmodium

X12 – Napier grass

Napier/Desmodium

Key: V Available X Not available **Table 3.** Availability of Crops

X6 – Napier

feed

X11 –

silage

X15 –

silage

pasture

pasture

X3 –

food stuffs grown at Uyole during the year.

January-February

\*\*\* Approximated the same as pasture grass, set stocking, close grazing.

Note: CP% means Crude Protein percentage, CPDC% means Crude Protein Digestibility Coefficient, ME MJ/kg DM means metabolizable energy in mega joules per kg of dry matter.

**Table 4.** Metabolizable Energy, Protein Content and Digestibility of Some of the Common Feeds at UAC

### **2.4. Nutrient value for the purchased concentrates**

Supplementary feeding by purchased concentrates is usually done to the milking cows in order to increase their milk output. This is done throughout the year. These concentrates are in the form of energy feeds and protein feeds. Their nutrient values are given in Table 2.5.

**Table 5.** Metabolizable Energy, Protein Content and Digestibility of the Concentrates

The yields of different crops and grasses for various fertilizer application levels are shown in Table 2.6 and 2.7. The total ME and DCP on the basis of ha can be estimated (see Table 2.8). The total ME and DCP for the purchased concentrates is estimated on the basis of tonnage (see Table 2.9)

\* The most efficient fertilizer application yield per kg. of dry matter.

**Table 6.** Approximate Nitrogen Efficiency for some of the Crops where Different levels of Fertilizer are applied at UAC

Dry matter yield and fertilizer applied figures were obtained from the UAC.

1 Phosphate was included.

252 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

Supplementary feeding by purchased concentrates is usually done to the milking cows in order to increase their milk output. This is done throughout the year. These concentrates are in the form of energy feeds and protein feeds. Their nutrient values are given in Table 2.5.

Maize meal 10.6 86 14.2 Maize bran 9.6 65 12.5 Rice Polishing 14.9 87 15.5

Cotton seed case (undecorticated) 23.1 77 8.5 Cotton seed case (decorticated) 41.7 72 10.8 Sunflower cake (undecorticated) 20.6 90 9.5 Sunflower cake (decorticated) 31.0 75 11.9 Lupin grain 33.7 81 14

The yields of different crops and grasses for various fertilizer application levels are shown in Table 2.6 and 2.7. The total ME and DCP on the basis of ha can be estimated (see Table 2.8). The total ME and DCP for the purchased concentrates is estimated on the basis of tonnage

Crop Fertilizer Applied kg N/ha DM Yield in kg/ha Nitrogen Efficiency kg

80 5500 31\* 160 7500 28 320 12000 28

120 2083 17

120 3515 29

120 5855 49

80 4720 59\* 160 7670 48 320 11370 36

80 4490 56\* 160 7280 46 320 15220 48

0 3000

Rhodes Pasture <sup>60</sup> <sup>1410</sup> 24\*

Rhodes Hay <sup>60</sup> <sup>3115</sup> 52\*

Rhodes Silage <sup>60</sup> <sup>3455</sup> 58\*

**Table 6.** Approximate Nitrogen Efficiency for some of the Crops where Different levels of Fertilizer are

\* The most efficient fertilizer application yield per kg. of dry matter.

DM/kg N

**Table 5.** Metabolizable Energy, Protein Content and Digestibility of the Concentrates

Type CP % CPDC % MEMJ/Kg DM

**2.4. Nutrient value for the purchased concentrates**

**Energy Feeds**

**Protein Feeds**

(see Table 2.9)

Natural Pasture

Napier Grass Silage

Napier Grass Greenfield

applied at UAC

**Table 7.** Approximate Yield of Different Crops and Grasses (Feeds) for the Most Efficient Fertilizer Levels

The figures for dry matter yield and fertilizer applied were obtained from Uyole Agricultural Centre (UAC).

Metabolizable energy and DCP in Table 2.8 were obtained by multiplying dry matter yield in Table 2.7 by MEMJ/kg DM CP% and CPDC% in Table 2.4 respectively..

#### **2.5. Fertilizer use and pasture production costs**

The primary inputs involved in crop production are fertilizer, labour and cost of seeds in certain types of crops.

By using nitrogen, the carrying capacity of the land is increased which directly affects the cost of production. The profitability of applying nitrogen depends on the relationship between the cost of inputs and the value of realized output in the form of livestock and livestock products.

Based on records from production at the UAC, the following costs (Table 2.10) are incurred in pasture production – seed, cultivation and planting costs distributed over five years (the leys/grown pasture assumed life time) and fertilizer application and harvesting costs for three yearly harvest.

\* Assumed same as lupin grain.

**Table 8.** Estimated Total Metabolizable Energy (ME) and Digestible Crude Protein (DCP) of some of the Commonly Grown Feeds per hectare at UAC

Note: Digestible Crude Protein (DCP) is a measure of the useful protein potential of the feed and has been calculated from the crude protein content and the crude protein digestibility of the feed. The nutritive value of each feed has been expressed in terms of its Metabolizable energy and the Digestible Crude Protein (DCP).

ME and DCP in Table 2.9 were obtained by multiplying 1000 by MEMJ/kg Dm, CP% and CPDC% in Table 2.5 respectively..

**Table 9.** Estimated Total Metabolizable Energy (ME) and Digestible Crude Protein (DCP) of the Purchased Concentrates per ton at UAC

**Table 10.** Pasture Production Input Cost at UAC. Source: Myoya ., 1980, p. 41.

The production costs are based on the following:

254 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

Natural Pastures 80 50600 382.3 Rhodes Grass 60 12267 65.6 Rhodes/Desmodium - 16590 124.7

Lupins 20P 57500 568.9 Oats 25N 10P 26250 254.6 Napier Grass 80N 46696 529 Napier/Desmodium - 48400 901

Rhodes Grass 60N 28035 174

Rhodes Grass 60N 26604 92.7 Rhodes/Desmodium - 15120 53.4 Maize 100N 20P 89000 277 Oats 25N 10P 21000 115.8 Lupins\* 20P 85200 1650 Napier Grass 40N 41536 483 Napier/Desmodium 35200 409.6

**Table 8.** Estimated Total Metabolizable Energy (ME) and Digestible Crude Protein (DCP) of some of

Type ME/ton DCP/ton

Maize Meal 14200 91.2 Maize Bran 12500 62.4 Rice Polishing 15000 129.6

Cotton Seed Cake (undecorticated) 8500 178 Cotton Seed Cake (decorticated) 10800 296.6 Sunflower Cake (undecortimated) 9500 185.4 Sunflower Cake (decorticated) 11900 232.5 Lupin Grain 14200 273

expressed in terms of its Metabolizable energy and the Digestible Crude Protein (DCP).

Note: Digestible Crude Protein (DCP) is a measure of the useful protein potential of the feed and has been calculated from the crude protein content and the crude protein digestibility of the feed. The nutritive value of each feed has been

ME and DCP in Table 2.9 were obtained by multiplying 1000 by MEMJ/kg Dm, CP% and CPDC% in Table 2.5

**Table 9.** Estimated Total Metabolizable Energy (ME) and Digestible Crude Protein (DCP) of the

values in MEMJ/ha DCP kg/ha

**Type** Fertilizer Level N kg Metabolizable Energy

**Pasture**

**Hay**

**Silages**

**Green Feed (Forage)**

\* Assumed same as lupin grain.

**Energy Feeds**

**Protein feeds**

respectively..

Purchased Concentrates per ton at UAC

the Commonly Grown Feeds per hectare at UAC

Note that at the time of this research, 100 T shs was approximately equivalent to 1 U.S. \$. Thus the estimated cost of production of various feeds is depicted in Table 2.11 below.

**Table 11.** Costs of Feeds per Hectare or per ton Depending on the Nature of Feed (grown or purchased) for most Efficient Fertilizer Applications.

### **3.**

#### **3.1. Setting up the Linear Programming (L.P.) model**

All together 23 different feeds were available at UAC under the land utilisation programme. The 23 different feeds include concentrates and minerals which are fed according to milk production. We denote the acreage of the different crop types for the most 'efficient' fertilizer application by Xj in hectares for the grown crops and by Yj in tons for the purchased feeds.

#### *3.1.1. The objective function*

The objective of the model is to determine the herd size that would maximize the net profit at UAC.

#### **3.2. The objective function coefficient**

#### *3.2.1. Milk output and its revenue*

According to the annual livestock report of 1984-85 of UAC, Gross income was 3.5 million Tshs. (90% was from dairy, excluding butter processing and cream). Gross income from dairy was 3.15 million T shs. The variable costs of production were 1.575 million T shs. Gross profit was therefore 1.575 million T shs. According to the same report the average number of cows was 100. Therefore the profit per cow was 15,750 T shs per annum**.**

#### *3.2.2. Milk production input costs*

In order to find the optimum herd size, it is important that the inputs i.e. crops involved in dairy production are included in the programme. As already seen earlier, various costs of production could be worked out.

The objective function is therefore to Maximize the Net Profit. Denote the different acreage for the grown crops types by X where j = 1, 2, …. 15 are grown crops in hectares, Yj for the purchased concentrates in tons where j ≥ 17 and by Zj for the herd size when j = 16 where,

For grown crops

256 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

Maize (per ha) 5820 Lupins (per ha) 5316 Oats (per ha) 5492 Napier Grass (per ha) 3849 Napier/Desmodium (per ha) 2480 Rhodes Grass (per ha) 3530 Rhodes/Desmodium 3048

Maize Meal 10000 Maize bran 4000 Rice Polishing 12000

Cotton Seed Cake (undecorticated) 6000 Cotton seed Cake (decorticated) 6000 Cotton Seed Cake (undecorticated) 6000 Sunflower Cade (undecorticated) 6000 Lupin Grain 8000

**Table 11.** Costs of Feeds per Hectare or per ton Depending on the Nature of Feed (grown or purchased)

All together 23 different feeds were available at UAC under the land utilisation programme. The 23 different feeds include concentrates and minerals which are fed according to milk production. We denote the acreage of the different crop types for the most 'efficient' fertilizer application by Xj in hectares for the grown crops and by Yj in tons for the

The objective of the model is to determine the herd size that would maximize the net profit

According to the annual livestock report of 1984-85 of UAC, Gross income was 3.5 million Tshs. (90% was from dairy, excluding butter processing and cream). Gross income from

**Silage**

ton)

**3.**

**Energy Feeds**

**Protein Feeds**

purchased feeds.

at UAC.

*3.1.1. The objective function*

**3.2. The objective function coefficient**

*3.2.1. Milk output and its revenue*

Purchased Foods Cost in Tshs (per

for most Efficient Fertilizer Applications.

**3.1. Setting up the Linear Programming (L.P.) model**

For Purchased Feeds

#### **Table 12.**

Using the cost values in Table 2.12, the objective function will be to

#### Maximize

At UAC, the objective is formulated on the basis of one type of breed only since there is only one breed at UAC for dairy production. In situations where multiple breeds are involved, a multiple objective function can be formulated in line with modified costs and profits accordingly.

#### **The Constraints**

#### *3.2.3. Land constraint*

Let the total acreage available be A. The acreage constraint ensures that the amount of land available for the growth of various crops is not exceeded.

$$\sum\_{j=1}^{15} \mathbf{X}\_j \quad \le A$$

where A is the total acreage in hectares

*Xj* is the acreage for different crop types j in hectares.

In the case of UAC, A is 790 hectares.

#### *3.2.4. Maintenance energy requirement constraint*

As a cow needs a minimum quantity of bulky food in its diet, it was decided that at least sufficient energy to supply maintenance requirements should come from food of this type, and should be grown on the farm.

Suppose crop j supplies *<sup>j</sup> a* kg of energy ( MJME) per ha. If one cow requires *mE* MJME for maintenance, then

$$\sum\_{j=1}^{15} a\_j X\_j \quad \ge \quad E\_m \, Z\_{16}$$

#### *3.2.5. Total energy requirement constraint*

Suppose crop j supplies *<sup>j</sup> a* megajoules of metabolizable energy per hectare and suppose the purchased concentrates do supply *<sup>j</sup> b* megajoules of metabolizable energy per ton. If one cow requires *<sup>l</sup> E* metabolizable energy for maintenance and lactation then.

$$\sum\_{j=1}^{15} a\_j \ X\_j + \sum\_{j=17}^{24} b\_j \ Y\_j \ge \ E\_l \ Z\_{16}$$

#### *3.2.6. Maintenance protein requirement constraint*

Suppose crop j supplies *<sup>j</sup> p* kg. of digestible crude protein per hectare. If one cow requires q kg. of Digestible Crude Protein for maintenance then.

$$\sum\_{j=1}^{15} p\_j \ge \mathbf{X}\_j \quad \ge q \, Z\_{16}$$

#### *3.2.7. Total protein requirement constraint*

Suppose crop j supplies *<sup>j</sup> p* kg. of digestible crude protein per hectare and suppose the purchased concentrated do supply *jr* kg. of digestible crude protein per ton. If one cow requires t kg. of digestible Crude Protein for maintenance and lactation

$$\text{Then } \sum\_{j=1}^{15} p\_j \, X\_j + \sum\_{j=17}^{24} r\_j \, Y\_j \quad \ge t \, Z\_{16}$$

#### *3.2.8. Space constraint*

258 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

At UAC, the objective is formulated on the basis of one type of breed only since there is only one breed at UAC for dairy production. In situations where multiple breeds are involved, a multiple objective function can be formulated in line with modified costs and profits

Let the total acreage available be A. The acreage constraint ensures that the amount of land

*X A*

As a cow needs a minimum quantity of bulky food in its diet, it was decided that at least sufficient energy to supply maintenance requirements should come from food of this type,

Suppose crop j supplies *<sup>j</sup> a* kg of energy ( MJME) per ha. If one cow requires *mE* MJME for

*jj m*

Suppose crop j supplies *<sup>j</sup> a* megajoules of metabolizable energy per hectare and suppose the purchased concentrates do supply *<sup>j</sup> b* megajoules of metabolizable energy per ton. If one

*j j jj l*

*aX bY EZ*

*aX E Z*

16

16

15

1

*j*

cow requires *<sup>l</sup> E* metabolizable energy for maintenance and lactation then.

15 24

*j j*

1 17

15

1 *j j*

available for the growth of various crops is not exceeded.

*Xj* is the acreage for different crop types j in hectares.

*3.2.4. Maintenance energy requirement constraint*

Maximize

accordingly.

**The Constraints**

*3.2.3. Land constraint*

where A is the total acreage in hectares

In the case of UAC, A is 790 hectares.

and should be grown on the farm.

*3.2.5. Total energy requirement constraint*

maintenance, then

Let the space needed for a cow on the average be s m 2. If the available space has a total area of h square metres then this particular farm can accommodate a maximum of M = h/s animals. Thus

$$\mathbf{Z}\_{16} \le \mathbf{M}$$

At UAC s = 6 m 2 area needed by one cow. H = 24,000 m 2 is area of the available shelter at UAC. Then M = h/s = 4000. The number of animals that can be 'accommodated'. Therefore

$$Z\_{16} \le 4000$$

Three L.P. models were run with different assumptions for each model. In the first model, the model was run for grown crops only. In the second model the imposed restriction was that maize should not be grown for the purpose of feeding animals (with an intuitive idea that maize should be for humans only). This was removed from the programme in the usual way by making its cost of production exorbitantly high. The problem was unchanged except for the coefficient C9 which was changed from 5820 to 99999. In the third model, the model was run for grown crops and purchased concentrates. The third model was feasible and gave the maximum profit. Thus the third model was adopted for our study. The solutions to the third model is presented in section 3. Together with the solution, post optimality analysis i.e. how sensitive is the optimal solution - and the appropriate interpretation are given for the this model.

We shall use the cost values in Table 2.12 and the net profit of 15,750 Tshs. per cow as calculated in section 3.2.1 for the objective function coefficients. The feed values in Table 2.9 and 2.10 will be used as the coefficients of the left hand side of crop and purchased constraints respectively while feed requirement values in Table 2.1 will be used as the coefficient of the Z on right hand sides of the constraints for the available feed supply periods as shown in Table 2.4. Our linear programming problem involving all the feeds (grown foods and purchased concentrates) is presented as follows:

#### Maximize

15750 Z16 - 1048X1 - 2353X2 - 2032X3 - 2566X4 - 3544X5 - 1653X6 - 3661X7 - 3530 X8 - 5820X9 - 3530X10 - 3048X11 - 3840X12 - 5492X13 - 5316X14 - 2480X15 - 10000Y17 - 4000Y18 - 12000Y19 - 8000Y20 - 6000Y21 - 6000Y22 - 6000Y23 - 6000Y24

Subject to

$$\sum\_{j=1}^{15} X\_j \le 790 \quad \text{land constraint} \tag{6}$$

$$Z\_{16} \le 4000 \text{ Fercing space constraint} \tag{7}$$

Total energy requirement constraint in January and February

$$\begin{aligned} &150600 \text{X}\_1 + 12267 \text{X}\_2 + 16590 \text{X}\_3 + 14200 \text{Y}\_{17} + 12500 \text{Y}\_{18} = 15000 \text{Y}\_{19} + \\ &+ 14200 \text{Y}\_{20} + 8500 \text{Y}\_{21} + 10800 \text{Y}\_{22} + 9500 \text{Y}\_{23} + 11900 \text{Y}\_{24} \geq 6073 \text{Z}\_{16} \end{aligned} \tag{8}$$

Maintenance energy requirement constraint in January and February

$$150600\text{X}\_1 + 12267\text{X}\_2 + 16590\text{X}\_3 \ge 2956\text{ Z}\_{16} \tag{9}$$

Total protein requirement constraint in January and February

$$\begin{aligned} \text{1382.3 X}\_{1} + 65.6 \text{X}\_{2} + 124.7 \text{X}\_{3} + 91.2 \text{Y}\_{17} + 62.8 \text{Y}\_{18} \text{129.6 Y}\_{19} + \\ + 273 \text{Y}\_{20} + 178 \text{Y}\_{21} + 296.6 \text{Y}\_{22} + 185.4 \text{Y}\_{23} + 232.5 \text{Y}\_{24} \ge 47.22 \text{ Z}\_{16} \end{aligned} \tag{10}$$

Maintenance protein requirement constraint in January and February

$$6382.3\,\mathrm{X}\_1 + 65.6\mathrm{X}\_2 + 124.7\mathrm{X}\_3 \ge 16.74\,\mathrm{Z}\_{16} \tag{11}$$

Total energy requirement constraint in December

$$\begin{aligned} &50600\mathbf{X}\_1 + 12267\mathbf{X}\_2 + 16590\mathbf{X}\_3 + 46696\mathbf{X}\_4 + 48400\mathbf{X}\_6 + 28035\mathbf{X}\_8 + 89000\mathbf{X}\_9 + \\ &+ 26604\mathbf{X}\_{10} + 15120\mathbf{X}\_{11} + 41536\mathbf{X}\_{12} + 35200\mathbf{X}\_{15} + 14200\mathbf{Y}\_{17} \\ &+ 15000\mathbf{Y}\_{19} + 14200\mathbf{Y}\_{20} + 85000\mathbf{Y}\_{21} = 10800\mathbf{Y}\_{22} + 9500\mathbf{Y}\_{23} + 11900\mathbf{Y}\_{24} \geq \\ &2 \geq 2812 \,\mathbf{Z}\_{16} \end{aligned} \tag{12}$$

Maintenance energy requirement constraint in December

$$\begin{aligned} &50600 \text{X}\_1 + 12267 \text{X}\_2 + 16590 \text{X}\_3 + 46696 \text{X}\_4 + 48400 \text{X}\_6 + 28035 \text{X}\_8 + \\ &+ 89000 \text{X}\_9 + 26604 \text{X}\_{10} + 15120 \text{X}\_{11} + 41536 \text{X}\_{12} + 35200 \text{X}\_{15} \geq 1478 \text{Z}\_{16} \end{aligned} \tag{13}$$

Total protein requirement constraint in December

260 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

(grown foods and purchased concentrates) is presented as follows:

15750 Z16 - 1048X1 - 2353X2 - 2032X3 - 2566X4 - 3544X5 - 1653X6 - 3661X7 - 3530 X8 - 5820X9 - 3530X10 - 3048X11 - 3840X12 - 5492X13 - 5316X14 - 2480X15 - 10000Y17 - 4000Y18 - 12000Y19 - 8000Y20 - 6000Y21 - 6000Y22

15

1

Maintenance energy requirement constraint in January and February

Maintenance protein requirement constraint in January and February

19 20 21 22

Maintenance energy requirement constraint in December

*j X*

Total energy requirement constraint in January and February

Total protein requirement constraint in January and February

Total energy requirement constraint in December

16

2812 Z

Maximize

Subject to

and 2.10 will be used as the coefficients of the left hand side of crop and purchased constraints respectively while feed requirement values in Table 2.1 will be used as the coefficient of the Z on right hand sides of the constraints for the available feed supply periods as shown in Table 2.4. Our linear programming problem involving all the feeds

790 land constraint *<sup>j</sup>*

1 2 3 17 18 19 20 21 22 23 24 16

1 2 3 17 18 19 20 21 22 23 24 16

12 34689 10 11 12 15 17 18

50600X 12267X 16590X 46696X 48400X 28035X 89000X 26604X 15120X 41536X 35200X 14200Y 12500Y +15000Y 14200Y 85000Y 10800Y 9500Y23 11900Y24

273Y 178Y 296.6Y 185.4Y 232.5Y 47.22 Z

382.3 X 65.6X 124.7X 91.2Y 62.8Y 129.6 Y

 (8)

50600X 12267X 16590X 14200Y 12500Y 15000Y 14200Y 8500Y 10800Y 9500Y 11900Y 6073 Z

(6)

Z 4000 Fencing space constraint <sup>16</sup> (7)

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>16</sup> 50600X 12267X 16590X 2956 Z (9)

<sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>16</sup> 382.3 X 65.6X 124.7X 16.74 Z (11)

(12)

(10)

$$\begin{aligned} &382.3\mathbf{X}\_1 + 65.6\mathbf{X}\_2 + 124.7\mathbf{X}\_3 + 529\mathbf{X}\_4 + 901\mathbf{X}\_6 + 174\mathbf{X}\_8 + 277\mathbf{X}\_9 + \\ &+ 92.7\mathbf{X}\_{10} + 53.4\mathbf{X}\_{11} + 483\mathbf{X}\_{12} + 409.6\mathbf{X}\_{15} + 91.2\mathbf{Y}\_{17} + 62.4\mathbf{Y}\_{18} + 129.6\mathbf{Y}\_{19} + \\ &+ 273\mathbf{Y}\_{20} + 178\mathbf{Y}\_{21} + 296.6\mathbf{Y}\_{22} + 185.4\mathbf{Y}\_{23} + 232.5\mathbf{Y}\_{24} \geq 21.33\mathbf{Z}\_{16} \end{aligned} \tag{14}$$

Maintenance protein requirement in December

$$\begin{aligned} &5382.3\text{X}\_1 + 65.6\text{X}\_2 + 124.7\text{X}\_3 + 529\text{X}\_4 + 901\text{X}\_6 + \\ &+174\text{X}\_8 + 277\text{X}\_8 + 92.7\text{X}\_{10} + 53.4\text{X}\_{11} + 483\text{X}\_{12} + 409.6\text{X}\_{15} \geq 8.37\text{Z}\_{16} \end{aligned} \tag{15}$$

Total energy requirement constraint in March and April

1 2 3 4 5 6 11 17 18 19 20 21 22 23 24 16 50600X 12267X 16590X 46696X 57500X 48400X 26250X +1400Y 12500Y 15000Y 14200Y 8500Y 10800Y 95500Y +11900Y 6509 Z (16)

Maintenance energy requirement constraint in March and April

$$50600\text{X}\_1 + 12267\text{X}\_2 + 16590\text{X}\_3 + 46696\text{X}\_4 + 57500\text{X}\_5 + 48400\text{X}\_6 + 26250\text{X}\_7 \ge 2956\text{z}\_{16} \tag{17}$$

Total protein requirement constraint in March and April

$$\begin{aligned} &382.3\mathbf{X}\_1 + 65.6\mathbf{X}\_2\\ &298.9\mathbf{X}\_1 + 62.6\mathbf{X}\_2 + 529\mathbf{X}\_4 + 569\mathbf{X}\_6 + 901\mathbf{X}\_6 + 256\mathbf{X}\_7 + 189.2\mathbf{X}\_{19} + 129.6\mathbf{X}\_{21} + 178\mathbf{X}\_{21} + 296.6\mathbf{Y}\_{22} + 185.4\mathbf{Y}\_{23} + 180.2\mathbf{Y}\_{34} + 232.5\mathbf{Y}\_{24} \geq \\ &+ 232.5\mathbf{Y}\_{24} \geq 51.25\mathbf{Z}\_{16} \end{aligned}$$

Maintenance protein requirement in March and April

$$6.382.3\text{X}\_1 + 65.6\text{X}\_2\\124.7\text{X}\_3 + 529\text{X}\_4 + 569\text{X}\_6 + 901\text{X}\_6 + 256\text{X}\_7 \ge 16.74\text{Z}\_{16} \tag{19}$$

Total energy requirement constraint in May

$$\begin{aligned} &50600\mathbf{X}\_1 + 12267\mathbf{X}\_2 + 16590\mathbf{X}\_3 + 46696\mathbf{X}\_4 + 57500\mathbf{X}\_5 + \\ &+ 48400\mathbf{X}\_6 + 26250\mathbf{X}\_7 + 89000\mathbf{X}\_9 + 14200\mathbf{Y}\_{17} + 12500\mathbf{Y}\_{18} + \\ &+ 15000\mathbf{Y}\_{19} + 14200\mathbf{y}\_{20} + 85500\mathbf{y}\_{21} + 10800\mathbf{Y}\_{22} + 9500\mathbf{Y}\_{23} + 11900\mathbf{Y}\_{24} \geq 3761\mathbf{Z}\_{16} \end{aligned} \tag{20}$$

Maintenance energy requirement constraint in May

$$\begin{aligned} &50600 \text{X}\_1 + 12267 \text{X}\_2 + 16590 \text{X}\_3 + 46696 \text{X}\_4 + \\ &+ 57500 \text{X}\_5 + 48400 \text{X}\_6 + 26250 \text{X}\_7 + 89000 \text{X}\_9 \ge 1478 \text{Z}\_{16} \end{aligned} \tag{21}$$

Total protein requirement constraint in May

$$\begin{aligned} &382.3\mathbf{X}\_1 + 65.6\mathbf{X}\_2 + 124.7\mathbf{X}\_3 + 529\mathbf{X}\_4 + 569\mathbf{X}\_4 + 901\mathbf{X}\_6 + 256\mathbf{X}\_7 + \\ &+ 91.2\mathbf{Y}\_{17} + 62.4\mathbf{Y}\_{18} + 129.6\mathbf{Y}\_{19} + 273\mathbf{Y}\_{20} + 178\mathbf{Y}\_{21} + 296.6\mathbf{Y}\_{22} + 185.4\mathbf{Y}\_{23} + \\ &+ 232.5\mathbf{Y}\_{24} \geq 30.55\mathbf{Z}\_{16} \end{aligned} \tag{22}$$

Maintenance protein requirement constraint in May

$$\begin{aligned} \text{382.3X}\_{1} + 65.6X\_{2} + 124.7X\_{3} + 529X\_{4} + 569X\_{4} + 901X\_{6} + \\ \text{+ 256X}\_{7} + 277X\_{9} \ge 8.37Z\_{16} \end{aligned} \tag{23}$$

Total energy requirement constraint in June

$$\begin{aligned} &46696\mathbf{X}\_4 + 57500\mathbf{X}\_5 + 48400\mathbf{X}\_6 + 26250\mathbf{X}\_7 + \\ &+ 89000\mathbf{X}\_9 + 14200\mathbf{Y}\_{17} + 12500\mathbf{Y}\_{18} + 15000\mathbf{Y}\_{19} + \\ &+ 14200\mathbf{Y}\_{20} + 8500\mathbf{Y}\_{21} + 10800\mathbf{Y}\_{22} + 9500\mathbf{Y}\_{23} + \\ &+ 11900\mathbf{Y}\_{24} \geq 3400\mathbf{Z}\_{16} \end{aligned} \tag{24}$$

Maintenance energy requirement constraint in June

$$46696\text{X}\_4 + 57500\text{X}\_5 + 48400\text{X}\_6 + 26250\text{X}\_7 + 89000\text{X}\_9 \ge 1478\text{Z}\_{16} \tag{25}$$

Total protein requirement constraint in June

$$\begin{aligned} &529\mathbf{X}\_4 + 569\mathbf{X}\_5 + 901\mathbf{X}\_6 + 256\mathbf{X}\_7 + 277\mathbf{X}\_9 \, 9.2\mathbf{Y}\_{17} + \\ &+ 62.4\mathbf{Y}\_{18} + 129.6\mathbf{Y}\_{19} + 273\mathbf{Y}\_{20} + 178\mathbf{Y}\_{21} + 296.6\mathbf{Y}\_{22} + \\ &+ 185.4\mathbf{Y}\_{23} + 232.5\mathbf{Y}\_{24} \ge 27.04\,\mathbf{Z}\_{16} \end{aligned} \tag{26}$$

Maintenance protein requirement constraint in June

$$529\text{X}\_4 + 569\text{X}\_5 + 901\text{X}\_6 + 277\text{X}\_9 \ge 8.37\text{Z}\_{16} \tag{27}$$

Total energy requirement constraint in July and August

$$\begin{aligned} &46696\text{X}\_4 + 57500\text{X}\_5 + 48400\text{X}\_6 + 89000\text{X}\_9 + 26604\text{X}\_{10} + 15120\text{X}\_{11} + \\ &+ 41536\text{X}\_{12} + 21000\text{X}\_{13} + 14200\text{Y}\_{17} + 12500\text{Y}\_{18} + 15000\text{Y}\_{19} + 14200\text{Y}\_{20} + \\ &+ 14200\text{Y}\_{20} + 8500\text{Y}\_{21} + 10800\text{Y}\_{22} + 9500\text{Y}\_{23} + 11900\text{Y}\_{24} + 85200\text{X}\_{14} + \\ &+ 35200\text{X}\_1 \ge 6266\text{Z}\_{16} \end{aligned} \tag{28}$$

Maintenance energy requirement constraint in July and August

$$\begin{aligned} &46696\text{X}\_4 + 57500\text{X}\_5 + 48400\text{X}\_6 + 89000\text{X}\_9 + 26604\text{X}\_{10} + \\ &+ 15120\text{X}\_{11} + 41536\text{X}\_{12} + 21000\text{X}\_{13} + 85200\text{X}\_{14} + 35200\text{X}\_{15} \geq \\ &\ge 2956\text{Z}\_{16} \end{aligned} \tag{29}$$

Total protein requirement constraint in July and August

$$\begin{aligned} &529\mathbf{X}\_4 + 569\mathbf{X}\_5 + 901\mathbf{X}\_6 + 277\mathbf{X}\_9 + 92.7\mathbf{X}\_{10} + 91.2\mathbf{Y}\_{17} + \\ &+ 62.4\mathbf{Y}\_{18} + 129.6\mathbf{Y}\_{19} + 273\mathbf{Y}\_{20} + 178\mathbf{Y}\_{21} + 296.6\mathbf{Y}\_{22} + \\ &+ 185.4\mathbf{Y}\_{23} + 232.5\mathbf{Y}\_{24} + 53.4\mathbf{X}\_{11} + 483\mathbf{X}\_{12} + 115.8\mathbf{X}\_{13} + 1650\mathbf{X}\_{14} + \\ &+ 409.6\mathbf{X}\_{15} \geq 48.9 \text{ Z}\_{16} \end{aligned} \tag{30}$$

Maintenance protein requirement constraint in July and August

$$\begin{aligned} &529\mathbf{X}\_4 + 569\mathbf{X}\_5 + 901\mathbf{X}\_\chi + 277\mathbf{X}\_9 + 92.7\mathbf{X}\_{10} + \\ &+ 53.4\mathbf{X}\_{11} + 483\mathbf{X}\_{12} + 115.8\mathbf{X}\_{13} + 1650\mathbf{X}\_{14} + \\ &+ 409.6\mathbf{X}\_{15} \ge 16.74\mathbf{Z}\_{16} \end{aligned} \tag{31}$$

Total energy requirement constraint in September, October and November

$$\begin{aligned} &46696\text{X}\_4 + 48400\text{X}\_6 + \text{OX7} + 28035\text{X}\_9 + 26604\text{X}\_{10} + \\ &+ 15120\text{X}\_{11}41536\text{X}\_{12} + 35200\text{X}\_{15} + 14200\text{Y}\_{17} + 12500\text{Y}\_{18} + \\ &+ 15000\text{Y}\_{19} + 14200\text{Y}\_{20} + 8500\text{Y}\_{21} + 10800\text{Y}\_{22} + 9500\text{Y}\_{23} + \\ &+ 11900\text{Y}\_{24} \geq 9172\text{Z}\_{16} \end{aligned} \tag{32}$$

Maintenance energy requirement constraint in September, October and November

$$\begin{aligned} &46696\text{X}\_4 + 48400\text{X}\_6 + 28035\text{X}\_8 + 89000\text{X}\Theta + \\ &+ 26604\text{X}\_{10} + 15120\text{X}\_{11} + 41536\text{X}\_{12} + 35200\text{X}\_{15} \geq 4434\text{Z}\_{16} \end{aligned} \tag{33}$$

Total protein requirement constraint in September, October and November

$$\begin{aligned} &529\mathbf{X}\_4 + 90\mathbf{1}\mathbf{X}\_6 + 174\mathbf{X}\_8 + 277\mathbf{X}\_9 + 92.7\mathbf{X}\_{17} + \\ &+ 91.2\mathbf{Y}\_{17} + 62.4\mathbf{Y}\_{18} + 129.6\mathbf{Y}\_{19} + 273\mathbf{Y}\_{20} + 178\mathbf{Y}\_{21} + \\ &+ 296.6\mathbf{Y}\_{22} + 185.4\mathbf{Y}\_{23} + 232.5\mathbf{Y}\_{24}\mathbf{5}3.4\mathbf{X}\_{11} + 484\mathbf{X}\_{12} + \\ &+ 409.6\mathbf{X}\_{15} \ge 71.15 \mathbf{Z}\_{16} \end{aligned} \tag{34}$$

Maintenance protein requirement constraint in September, October and November

$$\begin{aligned} &529\mathbf{X}\_4 + 90\mathbf{1}\mathbf{X}\_6 + 174\mathbf{X}\_8 + 277\mathbf{X}\_9 + 92.7\mathbf{X}\_{10} + \\ &+ 53.4\mathbf{X}\_{11} + 483\mathbf{X}\_{12} + 409.6\mathbf{X}\_{15} \geq 25.11 \,\mathbf{Z}\_{16} \end{aligned} \tag{35}$$

ALL X's, Y's and Z ≥ 0.

262 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

 1 2 3446 7 9 16

24 16

+ 11900Y 3400 Z

Maintenance energy requirement constraint in June

Maintenance protein requirement constraint in June

Total energy requirement constraint in July and August

1 16

16

Total protein requirement constraint in July and August

Maintenance energy requirement constraint in July and August

+ 35200X 6266 Z

2956 Z

Total protein requirement constraint in June

24 16

Maintenance protein requirement constraint in May

+ 256X 277X 8.37 Z

232.5Y 30.55 Z

Total energy requirement constraint in June

1 2 34467

382.3X 65.6.X 124.7X 529X 569X 901X

4567 9 17 18 19 20 21 22 23

<sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>9</sup> <sup>16</sup> 46696X 57500X 48400X 26250X 89000X 1478 Z (25)

<sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>9</sup> <sup>16</sup> 529X 569X 901X 277X 8.37 Z (27)

89000X 14200Y 12500Y 15000Y + 14200Y 8500Y 10800Y 9500Y

4 5 6 7 9 17 18 19 20 21 22

456910 11 12 13 17 18 19 20 20 21 22 23 24 14

4 5 6 9 10

46696X 57500X 48400X 89000X 26604X 15120X 41536X 21000X 85200X 35200X

11 12 13 14 15

46696X 57500X 48400X 89000X 26604X 15120X + 41536X 21000X 14200Y 12500Y 15000Y 14200Y + 14200Y 8500Y 10800Y 9500Y 11900Y 85200X

529X 569X 901X 256X 277X 9.2Y + 62.4Y 129.6Y 273Y 178Y 296.6Y

23 24 16

+ 185.4Y 232.5Y 27.04 Z

46696X 57500X 48400X 26250X

(23)

382.3X 65.6.X 124.7X 529X 569X 901X 256X + 91.2Y 62.4Y 129.6Y 273Y 178Y 296.6Y 185.4Y

17 18 19 20 21 22 23

(22)

(24)

(26)

(28)

(29)

#### **3.3. The stocking rate or the herd size model**

The L.P. problem for UAC was run using the OR software by Dennis and Dennis (1991).

One could run any number of models with different assumptions for each model. In our case, three LP models were considered with different assumptions for each model. The assumptions considered were running the LP with all grown crops included, concentrates excluded, running the LP with maize and concentrates excluded and running the LP with all grown crops and concentrates included. The purpose of doing this was to find out what combination of foods would give the maximum profit. This and the previous linear programming problems were run on an IBM PC using the OR software by Dennis and Dennis (1991). Here OR (Operations Research) is defined as the systematic application of quantitative methods, techniques, and tools to the analysis of problems involving the operation of the system. The aim is the evaluation of probable consequences of decision choices, usually under conditions requiring the allocation of scarce resources –funds, manpower, time, or raw materials (Daellenbach & George, 1978). The computer output tables are presented in Table 3.1. The simplex tableau for the grown crops and purchased concentrates is discussed.

Inclusion of concentrates results into a big profit of T shs. 58,752,345.70. The option of giving concentrates to cows has a significant impact on profit maximization at UAC as shown in Table 3.1 We recommend this model.

The following results were obtained after 15 iterations of the Simplex Algorithm.

**Table 13.** The Final Simplex Tableau displaying all the Feeds (Grown and Purchased Concentrates).

Optimal Profit = T.shs 58,752,345.717. S here refers to slacks.

Results show that land to be allocated for natural pastures is 361.234 hectares, Napier/Desmodium 184.378 hectares and maize production 244.388 hectares. Total land used for their production is therefore 790 hectares i.e. the whole land available is utilized. Concentrate supplementation is 85.545 tons of cotton seed cake (decorticated) and 407.174 tons of maize bran. Fencing land for the cows is fully utilized. Herd size is 4000 cows. Since whatever available land and fencing has been utilized under this programme and profit has been maximized, it was deemed reasonable to adapt this model.

#### **4.**

264 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

concentrates is discussed.

X1 X6 X9 Y22 Y18 Z16 S4 S6 S7

model.

Table 3.1 We recommend this model.

361.234 184.378 244.388 85.545<PHONE_NUMBER> 12468000<PHONE_NUMBER>8442.076

excluded, running the LP with maize and concentrates excluded and running the LP with all grown crops and concentrates included. The purpose of doing this was to find out what combination of foods would give the maximum profit. This and the previous linear programming problems were run on an IBM PC using the OR software by Dennis and Dennis (1991). Here OR (Operations Research) is defined as the systematic application of quantitative methods, techniques, and tools to the analysis of problems involving the operation of the system. The aim is the evaluation of probable consequences of decision choices, usually under conditions requiring the allocation of scarce resources –funds, manpower, time, or raw materials (Daellenbach & George, 1978). The computer output tables are presented in Table 3.1. The simplex tableau for the grown crops and purchased

Inclusion of concentrates results into a big profit of T shs. 58,752,345.70. The option of giving concentrates to cows has a significant impact on profit maximization at UAC as shown in

**Variable Quantity Variable Quantity Variable Quantity**

**Table 13.** The Final Simplex Tableau displaying all the Feeds (Grown and Purchased Concentrates).

Results show that land to be allocated for natural pastures is 361.234 hectares, Napier/Desmodium 184.378 hectares and maize production 244.388 hectares. Total land used for their production is therefore 790 hectares i.e. the whole land available is utilized. Concentrate supplementation is 85.545 tons of cotton seed cake (decorticated) and 407.174 tons of maize bran. Fencing land for the cows is fully utilized. Herd size is 4000 cows. Since whatever available land and fencing has been utilized under this programme and profit has been maximized, it was deemed reasonable to adapt this

Optimal Profit = T.shs 58,752,345.717. S here refers to slacks.

49054442.076 328539.771 389219.771 7179873.951 21391873.951 150004.182 288044.182 39922442.076 49054442.076 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S28 S30

The following results were obtained after 15 iterations of the Simplex Algorithm.

S8 S9 S10 S11 S12 S13 S14 S15 S16

#### **4.1. Sensitivity analysis**

#### *4.1.1. Abundant and scarce resources*

Associated with every LP; there is a corresponding optimization problem called the Dual Problem. The original problem is called the primal problem. The purpose of the dual in our case is to identify scarce and abundant resources and as such give recommendations if any. Dual values represent quite precisely the per unit increase in the objective function which would follow from an increase in the availability of the corresponding factors or resources.

It should be obvious, first of all, that an increased availability of a factor which is not fully used will only leave more of it unused and add nothing to the objective function and such a constraint has zero dual value – it is a free good. (Note that a good is free, not because it is not used, but because there is more available than is required. Air and water are the classical cases of free goods which would be very far from free if their availability were restricted).

To summarise, we can assert that if Yk represents the per unit increase in revenue from an increase in the availability of the k th factors, then a change in availability of Δk will lead to a change in revenue of YkΔk.

It is obvious that an increased availability of a factor which is fully utilized can add considerably to the value of the objective function. Land constraint is fully utilized and its dual value is positive (8003.55). Similarly fencing space for cows (constraint 2) is fully utilized, its dual value is positive (13107.383). So an increase in the land for crops and an increase in the space for the animals can still add considerably to the revenue of the enterprise by rearing more cows. Thus, per unit increase in the land acreage would increase the objective function by 8003.55 whereas per unit increase in the fencing space would increase the objective function by 13107.385 with all other coefficients in the problem remaining the same.

On the other hand, a small increase in the right-hand-side of an abundant resource constraint will only change the amount of slacks or surplus and will not affect the value of the objective function. Thus the shadow price for any non-binding constraint is zero.

The other constraints, for example constraint (4) and constraints (6) to (30) except constraints (27) and (29), are not so binding in our case since an increase in their availability will leave more of them unused and add nothing to the revenue and, as such, their dual values are zero.

Constraints (1), (2), (3), (5), (27), and (29) are binding in our case and as such their dual values are positive. They are therefore scarce resources. If we go back to the primal problem we will see that these aforementioned constraints have all their slack values equal to zero and their corresponding dual variables are positive.

266 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

**Table 14.** Dual values for the recommended programme (model three whereby grown crops and concentrates are included).

The scarce resources in our model are therefore land, fencing space, energy supply from January to February, protein supply from January to February, energy supply from September to November and protein supply from September to November. Energy and protein supplies are scarce from September to November because these are dry months in Mbeya Region and as such food is scarce during this period. Similarly the supply of food from January to February is not adequate in Mbeya Region.

As for the abundant resources these have dual values equal zero in their constraints. An abundant resource worth mentioning is energy supply from March to April. The slack of this constraint S11 has the value 7179873.953 in the primal. This slack is an indication of surplus food available during rainy season in Mbeya Region which is mostly pronounced in March and April.

#### *4.1.2. The objective function coefficients*

266 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

**Variable Dual solution or shadow price Constraint**  S1 8003.55 (1) S2 13107.385 (2) S3 .121 (3) S4 0 (4) S5 7.632 (5) S6 0 (6) S7 0 (7) S8 0 (8) S9 0 (9) S10 0 (10) S11 0 (11) S12 0 (12) S13 0 (13) S14 0 (14) S15 0 (15) S16 0 (16) S17 0 (17) S18 0 (18) S19 0 (19) S20 0 (20) S21 0 (21) S22 0 (22) S23 0 (23) S24 0 (24) S25 0 (25) S26 0 (26) S27 .146 (27) S28 0 (28) S29 2.851 (29) S30 0 (30)

**Table 14.** Dual values for the recommended programme (model three whereby grown crops and

from January to February is not adequate in Mbeya Region.

The scarce resources in our model are therefore land, fencing space, energy supply from January to February, protein supply from January to February, energy supply from September to November and protein supply from September to November. Energy and protein supplies are scarce from September to November because these are dry months in Mbeya Region and as such food is scarce during this period. Similarly the supply of food

concentrates are included).

It is important for us to know, for example, for what ranges of prices of the inputs in the objective function is the solution still optimal. To do this we assume the coefficient matrix A and the right hand side constraints b are unchanged but the profits vector c is changed to c+λc, where λ is any constant. The results are presented in Table 4.2.

**Table 15.** Sensitivity Analysis of Objective Function Coefficients

Of interest are the coefficients of the variables X1, X6, X9, Y18, Y22 and Z16. the lower and upper limits within which the solution is still optimal are shown in Table 4.2.

For example, the solution is still optimal so long as -9043.741 < C1< 20358.836 and so on. The cost (C1) of natural pasture in the objective function is -1048 per hectare. As long as this cost lies between -9043-741 and 20358..836 the solution is still optimal so long as the other costs C1's remain as they were in the primal.

#### **4.2. The right-hand-side ranges**

The right-hand-side ranges provide limits within which the objective coefficients of the dual problem are allowed to change without changing the solution. For changes outside the range the problem must be resolved to find the new optimal solution and the new dual price. We call the range over which the dual price is applicable the range of feasibility.

Assuming A and c are unchanged, b changes to b+b where is any constant, the right-hand side ranges within which the objective function remains optimal are presented in table 4.3.

**Table 16.** Sensitivity Analysis of Right Hand Ranges

Of interest are constraints (1), (2), (3), (5), (27) and (29) i.e., land for cultivation, fencing space, energy and protein supply from January to February and energy and protein supply from September to November constraints. These are the binding constraints in our model. As shown in Table 4.3, the ranges of constraints (1) and (2) are all positive i.e. 174.04 < Land size < 983.61 and 3212.67 < fencing space < 18158.99 and so on. For example, land size could be increased up to 983.61 hectares so long as the A matrix and the objective function vector are unchanged. The solution would still be optimal. An increase of one hectare of land would increase the objective function by 8003.55 as provided for by the dual.

Changes in the right-hand side of the constraints show how the optimal solution and net profit would change if we could obtain additional land or fencing space.

## **5. Conclusion**

268 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

C1's remain as they were in the primal.

**4.2. The right-hand-side ranges**

For example, the solution is still optimal so long as -9043.741 < C1< 20358.836 and so on. The cost (C1) of natural pasture in the objective function is -1048 per hectare. As long as this cost lies between -9043-741 and 20358..836 the solution is still optimal so long as the other costs

The right-hand-side ranges provide limits within which the objective coefficients of the dual problem are allowed to change without changing the solution. For changes outside the range the problem must be resolved to find the new optimal solution and the new dual price. We call the range over which the dual price is applicable the range of feasibility.

Assuming A and c are unchanged, b changes to b+b where is any constant, the right-hand side ranges within which the objective function remains optimal are presented in table 4.3.

Constraint Lower Limit Original Value Upper Limit 1 174.02 790 983.61 2 3212.67 4000 18158.99 3 -3640461.74 0 5212071.15 4 -12468000 0 NO LIMIT 5 -84149.1 0 21767.12 6 121920 0 NO LIMIT 7 43718442.08 0 NO LIMIT 8 4905442.08 0 NO LIMIT 9 328539.77 0 NO LIMIT 10 -389219.77 0 NO LIMIT 11 -7179873.95 0 NO LIMIT 12 -21391873.95 0 NO LIMIT 13 -150004.18 0 NO LIMIT 14 -288044.18 0 NO LIMIT 15 -39922442.08 0 NO LIMIT 16 -49054442.08 0 NO LIMIT 17 -300499.77 0 NO LIMIT 18 -389219.77 0 NO LIMIT 19 -23088000 0 NO LIMIT 20 -30776000 0 NO LIMIT

The model has managed to ascertain the profitability of a dairy farm. Indeed, this form of argument can be useful in the management of dairy farms of similar traits elsewhere. The assumption here is that the herd size was kept constant throughout the year. Perhaps this is an oversimplification but it provides a starting point. There is a need of formulating Operational Research models for which the need for having a fixed herd size can be relaxed. As can be seen from the input parameters of the L.P., the values are probably not in line with dynamics of time and technological advancement of raring /keeping dairy cattle. Perhaps there is a need of updating the input parameters so that they can match with time from farm to farm.

## **Author details**

Rocky R.J. Akarro *University of Dar es Salaam, Tanzania*

#### **6. References**

Konandreas P.A. & Anderson, F.M. (1982). Cattle herd dynamics: an integer and stochastic model for evaluating production alternatives. *ILCA (International Livestock Centre for Africa)* . Research Report No 2. Addis Ababa, Ethiopia.

270 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

Akarro, R.R.J. (1995).. An Operational Study of Dairy Farming in Tanzania. *Unpublished*

Akarro, R.R.J. (2009). Milk Breed Selection in Selected Farms in Tanzania by the Use of Simulation Techniques. *European Journal of Scientific Research,* Volume 34 Issue 1, July,

Balch, C.C.(1976). Ruminant digestion and nutritive value pages 214 – 218 in P.V.Fonnesbeck, L.E.Harris & L.C.Kearl, eds. *Proc.of the 1st Int. .Symp. on Feed composition. Animal Nutrient Requirements and Computerization of diets.* Utah Agr. Exp.

Daellenbach, H.G. & George, J.A (1978). *Introduction to Operations Research Techniques.* Allyn

Dennis,T.L. & Dennis, L.B .(1991). *Decision Support Software/ Management Science. Linear*

Blaxter,K.L.(1969). The efficiency of energy transformation in ruminants. In K.L. Blaxter, J.Klelanowski & G.Thorbek eds. *Energy metabolism of farm animals.* London, Routledge

Blaxter,K.L.(1973). Metabolizable energy and feeding system for ruminants. In H. swan & D. Lewis, eds. *Proc. Of Nutrition Conf. for Feed manufacturers No 7.* London,

Bredon, R.M. (1963). Feeding livestock in Africa, quoted by Kurwijila, R.L. (1991). *Dairy Production and management Vol. I. Basic husbandry and management practices under Tropical*

Hunt, L.A.(1966). Ash and energy content of material from several forage grasses. *Crop*

ILCA (1978) (International Livestock Centre for Africa). *Mathematical Modelling of Livestock Production Systems. Application of the Texas A & M. University beef cattle production model*

Kay, M. (1976).. Meeting the energy and protein requirements of the growing animal. In H. Swan & W.H.Broster, eds. *Principles of Cattle Production.* London, Butterworths. Kearl, L.C. (1982). Nutrient requirements of Ruminants in Developing Countries. *International Feed Stuffs Institute.* Utah Agric. Exptal. Stat; Utah State University; Logan,

Kifaro, G.C. & Akarro, F.M.N.(1987). Livestock Research in Southern Highland of Tanzania. Past constraints and future prospects, *Paper presented at the National Workshop on*

*Environment.* Lecture notes compendium for B.Sc. courses at SUA.

Annual livestock report of 1984-85 of UAC. *Unpublished Report, UAC.* Mbeya, Tanzania. Armstrong, D.G.(1964). Evaluation of artificially dried grass as a source of energy for

**6. References**

2009.

& Bacon, Inc.

Butterworths.

*Science,* 6:507-509.

Utah.

and Regan Paul, 21-28.

*Ph.D. thesis, University of Dar es Salaam.*

sheep.2. *J. Agric. Sci. Camb.* 62: 399 -417.

Sta., Utah State University, Logan.

Gohl, BO. (1981) *Tropical Feeds,* FAO, Rome.

*to Botswana.* System Studies No 1: Addis Ababa.

*Agricultural Research in Tanzania,* 1987. Arusha, Tanzania.

*Programming.* Copyright 1991, West Publishing Co.

Webster, A.J.F.(1978). Prediction of the energy requirements for growth in beef cattle. *Wld. Rev. Nutr. Diet.* 30: 189-226.

## **Dissemination of Scientific Data for Sustainable, Organic Milk Production Systems**

Sezen Ocak and Sinan Ogun

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51739

## **1. Introduction**

272 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

*Rev. Nutr. Diet.* 30: 189-226.

Webster, A.J.F.(1978). Prediction of the energy requirements for growth in beef cattle. *Wld.*

Most ecologically sustainable or organic agricultural projects concerning "Milk Production" have not been monitored comprehensively or been subjected to stringent evaluation methods to allow the outcomes to be regarded as scientifically acceptable. There is a strong need to not only promote such dairy projects but to collect, scrutinize and share the information in an appropriate scientific manner to encourage more widespread acceptance.

Researchers dealing with organic production have been more interested in solving practical problems than publishing papers, as such it makes it difficult to do comparative analysis with conventional productions systems and draw general conclusions regarding the nutritional value of dairy produce or health and well-being of livestock.

Despite the lack of reliable data on the benefits of organic produce from around the globe, the organic dairy sector is reported to be growing at between 15 to 23 percent a year in the countries assessed in this study, namely; Europe, USA, Australia and New Zealand. It is expected that by 2015, 25-30 percent of consumers of dairy products in the above nations will ensure that their regular purchases will be organic (Lohr, 1998).

In addition to the human health benefits, organic dairy farming aims to create more holistic, agro-ecological systems. Therefore the aim is not only to produce nutritious and chemical free produce but to ensure a sustainable management of natural resources where these products are produced. Animal health and welfare are also important elements of such a system (Lund & Rocklinsberg, 2001). This is a factor that is clearly recognized by the International Federation of Organic Agricultural Movements (IFOAM), the organization setting the basic standards for what can be labeled as organic.

The aim of this study is to review some of the relevant research carried out in this field and to assess suitable methods to disseminate such scientific data in a standardized, reliable and

an easily accessible manner to farmers needing this information. The information should be reliable enough to inform the conventional farmer of the benefits and shortfalls if they are considering organic production, or at least provide resource material for them to pursue further research into the topic.

Marketing and consumption of organic produce also being an important factor in the decisions of a potential producer; the study also evaluated numerous factors that may be the cause of the global shift toward the increased consumption of organic produce.

Besides the generally accepted health benefits of organic products, the contemporary, educated and well informed consumer is also trying to make a statement about the environmental benefits of organic production. They are asking from the producer/supplier to further inform them about food miles, efficient energy use, water pollution, soil conservation, carbon credits, natural resource management and alike. The study discovered that further effort was required on how information about consumer preference could be relayed back to the farmer.

Besides general scientific literature on organic dairy farming carried out by few very committed organizations and some institutions the authors also looked at a number of farms in the USA and Australia as case study farms to see if they were open to sharing relevant information about their outcomes. These farms were selected based on the importance they gave to the principles of sustainable organic production, such as; diversified farming measures and the use of crop rotations, resilient production systems based on diverse cultural system, minimal use of external agrochemical inputs, minimal use of pharmaceuticals for animal health issue by encouraging preventative measures rather than curative ones, emphasis on the use of local resources, recycling organic wastes, reduced environmental impact, reduced use of mechanization, utilization of small areas for cultivation and encouraging the use and preservation of traditional skills.

The producers who apply these principles have a very limited database of information on which to rely on, in addition the information would not stand up to the rigors of intensive scientific scrutiny. The study has provided numerous resources in its acknowledgment and reference list, which supports the principles of a holistic and dynamic production systems, but would strongly encourage further research in the field.

## **2. Farming trends**

In the present market place with heightened scrutiny on how food is produced, the conventional dairy farm unit is going through a major shift from mid-size farms to very small and very large ones - this is particularly the case in USA (Benbrook, 2009). In the very large size farms the cows do not have access to sufficient pasture to contribute significantly to their daily feed intakes, therefore grain-based rations and high-quality alfalfa (lucerne) hay form the backbone of the cows' diet. However in contrast to this trend the number and importance of small to moderate-scale organic dairy farms is increasing. The most successful operations grow all or most of their feed on or near the home farm. In addition, pasture and grazing contributes significantly to daily feed intakes in those parts of the year when the weather supports active forage plant growth. On conventional, feedlot-based industrial dairies, corn and other corn-based feeds typically account for around two-thirds of a cow's diet, whereas on grazing-based organic farms, pasture and forage-based feeds typically account for at least two-thirds of daily feed intake, and corn in all its forms less than onequarter.

On large conventional dairies, artificial insemination is used on mostly purebred Holstein cows. Each milking dairy animal is expected to produces about 10 to 11,000 liters of milk during a 305-day lactation period (Benbrook, 2009). A range of drugs are routinely administered to these animals to help them fight infections, efficiently digest their energy-dense, low-fiber feed, and to help synchronize artificial insemination breeding attempts.

On most small and moderate scale organic dairies, production levels are lower, averaging closer to 8,000 liters per year. Breeds of cattle other than Holsteins, as well as crossbreed cattle are common and artificial insemination is a tool used on many farms, but has not replaced bulls and traditional breeding programs.

However the authors have struggled to find sufficient research results in the agricultural economic domain to support this concept of a more long-term productive and a cost efficient production system in that of organic dairies. The few case study farms that were looked at certainly had the figures but were reluctant to share the results assumedly with the fear of losing their premium market edge. Due to the lack of actual accounting figures, its difficult to ascertain whether a shift in the supply – demand curve of organic milk in the market place would affect the profitability of organic farming in the long run. Presently the price premium is based solely on the availability of organic milk. It would appear however that if more people consumed organic milk and as such the health benefits became more evident than this could result in increase in consumption of organic milk products, meaning higher demand maintaining the high value in the market place.

## **3. Organic vs. conventional vs. biodiversity**

274 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

cause of the global shift toward the increased consumption of organic produce.

cultivation and encouraging the use and preservation of traditional skills.

but would strongly encourage further research in the field.

further research into the topic.

relayed back to the farmer.

**2. Farming trends**

an easily accessible manner to farmers needing this information. The information should be reliable enough to inform the conventional farmer of the benefits and shortfalls if they are considering organic production, or at least provide resource material for them to pursue

Marketing and consumption of organic produce also being an important factor in the decisions of a potential producer; the study also evaluated numerous factors that may be the

Besides the generally accepted health benefits of organic products, the contemporary, educated and well informed consumer is also trying to make a statement about the environmental benefits of organic production. They are asking from the producer/supplier to further inform them about food miles, efficient energy use, water pollution, soil conservation, carbon credits, natural resource management and alike. The study discovered that further effort was required on how information about consumer preference could be

Besides general scientific literature on organic dairy farming carried out by few very committed organizations and some institutions the authors also looked at a number of farms in the USA and Australia as case study farms to see if they were open to sharing relevant information about their outcomes. These farms were selected based on the importance they gave to the principles of sustainable organic production, such as; diversified farming measures and the use of crop rotations, resilient production systems based on diverse cultural system, minimal use of external agrochemical inputs, minimal use of pharmaceuticals for animal health issue by encouraging preventative measures rather than curative ones, emphasis on the use of local resources, recycling organic wastes, reduced environmental impact, reduced use of mechanization, utilization of small areas for

The producers who apply these principles have a very limited database of information on which to rely on, in addition the information would not stand up to the rigors of intensive scientific scrutiny. The study has provided numerous resources in its acknowledgment and reference list, which supports the principles of a holistic and dynamic production systems,

In the present market place with heightened scrutiny on how food is produced, the conventional dairy farm unit is going through a major shift from mid-size farms to very small and very large ones - this is particularly the case in USA (Benbrook, 2009). In the very large size farms the cows do not have access to sufficient pasture to contribute significantly to their daily feed intakes, therefore grain-based rations and high-quality alfalfa (lucerne) hay form the backbone of the cows' diet. However in contrast to this trend the number and importance of small to moderate-scale organic dairy farms is increasing. The most successful operations grow all or most of their feed on or near the home farm. In addition, pasture and Organic farming demonstrates clear advantages for biodiversity over conventional farming. Depending on altitude, organic farms have between 46 and 72 percent more semi-natural habitats and host 30 percent more species and 50 percent more individuals than non-organic farms (Source: FiBL). The lower farming intensities and higher proportion of semi-natural areas enable site-typical plant and animal species to exist on organic farms and allow farmers to benefit from an intact and therefore sustainably functioning ecosystem.

Agricultural policies are increasingly promoting ecologically-oriented farming methods that preserve biodiversity and conserve natural resources (FAO, 2002). Intensive farming by introduction of exotic species, land clearing, vegetation fragmentation, habitat change and soil erosion has been one of the main causes of biodiversity decline. (Bengtsson et al., 2005; Hole et al., 2005). Specific contributing factors to this decline with conventional farming have been; indiscriminate use of pesticides and synthetic fertilizers, land consolidation, drainage as well as the use of heavy machinery.

Numerous comparative studies showing the impact of conventional and organic farming systems verify the positive effect organic farming has on flora and fauna on field and also farm level (Fuller et al., 2005, Hole et al., 2005). A comprehensive analysis of 66 scientific studies shows that organically farmed areas have on average 30 percent more species and 50 percent more individuals than non-organic areas (Bengtsson et al., 2005). The positive effect of organic farming is most significant in cleared landscapes, but is also seen in structurally rich regions (Gabriel et al., 2006; Gabriel et al., 2010).

In particular birds, predatory insects, spiders, soil dwelling organisms and field flora benefit most from organic management as can be seen in **Figure 1** below. Pests and indifferent organisms on the other hand occur in similar numbers in the various farming systems. The differences in species diversity are especially noticeable with arable and horticulture crops in valleys – the differences seen in grassland are less pronounced. Comparison studies in mountainous regions are scarcely existing.

**Figure 1. Impact of Organic Farming on Biodiversity** - Number of studies that show organic farming having a positive (green bar), negative (red bar) or no effect (number in white circle) on biodiversity of various animal and plant groups in comparison to non-organic farm management. Summary of 95 scientific publications. **(Source: FiBL)**

To preserve rare and endangered species, adapted species protection programs are frequently necessary. The typical ecological compensation programs for farmland are not sufficient. Organic farming in combination with valuable semi-natural areas can therefore significantly contribute to improving species numbers (Pfiffner et al., 2003). Sky larks (Photo 1), a typical species that have been suppressed through intensification of farming, as well as the now rare lapwings, partridges, and whinchats, achieve higher population densities on organically managed farms (NABU, 2004; Neumann et al., 2007). Rare plant species on agricultural land (Gabriel et al., 2006; Gabriel et al., 2007) and ground beetles (Pfiffner et al., 2003) are also proven to be in higher diversity and density on organic farms.

276 Milk Production – Advanced Genetic Traits, Cellular Mechanism, Animal Management and Health

drainage as well as the use of heavy machinery.

rich regions (Gabriel et al., 2006; Gabriel et al., 2010).

mountainous regions are scarcely existing.

scientific publications. **(Source: FiBL)**

have been; indiscriminate use of pesticides and synthetic fertilizers, land consolidation,

Numerous comparative studies showing the impact of conventional and organic farming systems verify the positive effect organic farming has on flora and fauna on field and also farm level (Fuller et al., 2005, Hole et al., 2005). A comprehensive analysis of 66 scientific studies shows that organically farmed areas have on average 30 percent more species and 50 percent more individuals than non-organic areas (Bengtsson et al., 2005). The positive effect of organic farming is most significant in cleared landscapes, but is also seen in structurally