Example 3: Using the Simplex Tableau

The simplex method is a simple and elegent algorithmic engine for solving linear programs.  This example will help in the understanding of the mechanics of the simplex tableau.  The first step is to find an initial cornerpoint feasible solution.  The Acme Bicycle Company problem is a standard form LP, therefore the origin is a feasible cornerpoint.  Below is the simplex tableau for the basic feasible solution for the Acme Bicycle Company problem at the origin.

To begin, select the pivot column by clicking on a radio button below a column.  To find the minimum ratio value, press the Calculate button.  Select the pivot row by clicking on a radio button to the right of a row and press the Pivot button.  You are finished when there are no more negative values in the objective function row.

 

Basic Variable Equation Z x1 x2 x3 x4 x5 RHS MRT
Z 0 1  -15  -10  0   0  0    0 ____
x3 1 0   1  0   1  0  0  2 -
x4 2 0  0   1  0   1  0  3 -
x5 3 0   1   1  0  0   1  4 -