<prompt> Theha bothata ba linear programming bo eketsang phaello ea ho rekisa sehlahisoa se itseng.nan  <response>: Instruction in English: Construct a linear programming problem that maximizes the profit from selling a certain product. . Response in English: A company produces a certain product that it sells at a profit. The company aims to maximize its profit while taking into account its production constraints. In this scenario, linear programming can be used to determine the optimal level of production that will yield the maximum profit.Let x represent the number of products produced.Objective Function:The company wants to maximize its profit function P ax, where a is the profit per product.Constraints:1. Production capacity: The production capacity of the company is limited due to the available resources such as labor, raw materials, and machinery. This constraint is represented by the inequality x b, where b is the maximum production capacity of the company.2. Market demand: The market demand for the product is another factor that impacts production. The company cannot produce more than the market demands. This constraint is represented by the inequality x c, where c is the market demand for the product.Thus, the linear programming problem can be stated as follows:Maximize: P axSubject to:x b production capacityx c market demandx 0 non-negativity constraintThe solution to this linear programming problem will determine the optimal production level x that will yield the maximum profit for the company. . Response in Sesotho: Khampani e hlahisa sehlahisoa se itseng seo e se rekisang ka phaello. Khamphani e ikemiselitse ho eketsa phaello ea eona ha e ntse e ela hloko lithibelo tsa eona tsa tlhahiso. Boemong bona, ho ka sebelisoa lenaneo la linear ho fumana boemo bo nepahetseng ba tlhahiso bo tla hlahisa phaello e ngata. E re x e emele palo ea lihlahisoa tse hlahisoang. Mosebetsi oa sepheo: Khampani e batla ho eketsa tsebetso ea eona ea phaello P selepe, moo phaello e leng teng ka sehlahisoa ka seng. Litšitiso: 1. Bokhoni ba tlhahiso: Bokhoni ba tlhahiso ea khamphani bo lekanyelitsoe ka lebaka la lisebelisoa tse fumanehang joalo ka basebetsi, lisebelisoa tse tala le mechini. Tšitiso ena e emeloa ke ho se lekane x b, moo b e leng matla a phahameng a tlhahiso ea khamphani. 2. Tlhokahalo ea maraka: Tlhokahalo ea maraka bakeng sa sehlahisoa ke ntlha e ngoe e amang tlhahiso. Khampani ha e khone ho hlahisa ho feta litlhoko tsa maraka. Tšitiso ena e emeloa ke ho se lekane x c, moo c e leng tlhokahalo ea maraka bakeng sa sehlahisoa. Ka hona, bothata ba lenaneo la linear bo ka boleloa ka tsela e latelang: Eketsa: P selepe Ho ea ka: x b bokhoni ba tlhahiso x c tlhoko ea maraka x 0 thibelo e seng negativity Tharollo ea bothata bona ba linear programming e tla etsa qeto ea boemo bo nepahetseng ba tlhahiso x e tla fana ka phaello e ngata bakeng sa khamphani. 