Consider the following LP:

Maximize z = 3x1 + 2x2 + 3x3

Subject to

2x2 + x2 + x3 ‰¤ 2

3x1 + 4x2 + 2x3 ‰¥ 81

X1, x2, x3 ‰¥ 0

The optimal simplex tableau at the end of Phase I is given as

Explain why the non-basic variables X₁ > X₃, X₄, and X₅ 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.

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R Solution -5 0 -40 R-5 4