*7. Consider the following LP:

Maximize z = 3x\ + 2x2 + 3X3 subject to 2x\ + X2 + x3:5 2 3x] + 4X2 + 2X3 2: 8 The optimal simplex tableau at the end of Phase I is given as Basic Xl X2 X3 X4 Xs R Solution Z -5 0 -2 -1 -4 0 0 X 2 2 1 1 0 1 0 2 R -5 0 -2 -1 -4 1 0 Explain why the nonbasic variables Xl> X3, X4, and Xs can never assume positive values at the end of Phase II. Hence, conclude that their columns can dropped before we start Phase II. In essence, the removal of these variables reduces the constraint equations of the problem to X2 = 2. This means that it will not be necessary to carry out Phase II at all, because the solution space is reduced to one point only.

8. Consider the LP model Minimize z = 2Xl - 4X2 + 3x3 subject to 5x\ - 6X2 + 2X3 2: 5

- Xl + 3X2 + 5x3 2: 8 2Xl + 5X2 - 4x3