Example LP5:  Two Phase Simplex Tableau


For this example, the Acme Bicycle Company problem has been altered.  The metal finishing machine limit has been changed to the equality:  .  This problem is no longer a standard form linear program.

Below is the two phase tableau for the altered ABC problem.  To begin, select the pivot column by clicking on a radio button below a column.  Press the Calulate button to calculate the minimum ratios.  Select the pivot row by clicking a radio button to the right of a row and press Pivot.

Iterate until the artificial variables are forced to zero.  This will complete phase 1 and you will be in the feasible region.  Continue iterating just as in the previous example to find the optimum point.

Note that if you select x1 as the first entering basic variable then phase 2 finishes at the same time as phase 1.  However, if you select x2 as the first entering basic variable, then you must also iterate in phase 2 before the optimum is reached.  Try both!

You are currently in Phase 1.

Basic Variable Equation W Z x1 x2 s1 s2 a1 RHS MRT
W phase 1 -1 0  -1  -1  0  0  0  -4 ____
Z phase 2 0  1  -15  -10  0  0  0  0 ____
s1 1 0  0  1  0  1  0  0  2 -
s2 2 0  0  0  1  0  1  0  3 -
a1 3 0  0  1  1  0  0  1  4 -