Consider the following LP:

Maximize z = 3x1 + 2x2 + 3x3 subject to 2x1 + x2 + x3 … 2 3x1 + 4x2 + 2x3 Ú 8 x1, x2, x3 Ú 0 The optimal simplex tableau at the end of Phase I is Basic x1 x2 x3 x4 x5 R Solution r -5 0 -2 -1 -4 0 0 x2 2 1 1 0 1 0 2 R -5 0 -2 -1 -4 1 0 Explain why the nonbasic variables x1, x3, x4, and x5 can never assume positive values at the end of Phase II. Hence, conclude that their columns can be dropped before we start Phase II. In essence, the removal of these variables reduces the constraint equations of the problem to x2 = 2—meaning that it is not necessary to carry out Phase II in this problem.