Simple Pivot Tool

Go general:     Constraints = , Variables = .     Labels: ,    

Seed =  

Or:     Select an Exercise from Linear Programming: Foundations and Extensions:


Number format:     Zero Visibility:

Current Dictionary



This pivot tool can be used to solve linear programming problems.

By default, problems are assumed to have four variables and three constraints. To solve a problem of a different size, edit the two text fields to specify the number of rows and columns you want.

You can enter data elements into each text field to define a specfic problem. Alternatively, you can click on Generate Random Problem to quickly get a random problem to play with.

To make a pivot, simply click on the variable-button that you want to pivot around. If you click on a button associated with a zero pivot element, the applet will complain.

Primal infeasible right-hand side coefficients are highlighted in fuscia (after the first pivot) as are dual infeasible cost coefficients. When all the fuscia cells are gone, you have an optimal dictionary.

The Labels tab allows you to select the labels for the variable names making it easy to set up some standard variants of the simplex method. If the Dual labels are chosen and the Seed value is nonzero, then the matrix entries will be the negative transpose of the values one would get with Primal labels. If the Seed is a four-digit number (or smaller), the initial dictionary will be primal feasible and (usually) dual infeasible. If, on the other hand, the Seed value is a five-digit number, the initial dictionary will be dual feasible and (usually) primal infeasible.

The Seed value controls how random problems are generated. With the default value of zero, the random number generator is seeded according to the system clock. Specifying a nonzero seed value gives random problems that can be repeated by starting over with the same seed value.

The variable names are editable. To change the name of one of the xj's, just click on it as it appears in the objective function. Similarly, to change the name of a slack variable, wi, just click on the variable as it appears on the left side of its defining equation.

The Number format tab allows you to choose how you would like numbers to be displayed. There are three choices: (1) as fractions, (2) as floating point numbers, or (3) as integers. The third choice is accomplished by multiplying all the equations by the largest common denominator.

Click here for a fancier version of the pivot tool which includes artificial primal and dual objectives that enable one to do two phase methods directly with the tool.

Finally, click here for the Java Applet version of the same tool.

Acknowledgements: I'd like to thank former and current students, especially Hande Benson and Alex Yablonski, for their helpful suggestions and comments.