8. Consider the following LP:

Maximize z = 16xI + 15x2 subject to 40XI + 31x2 :5 124

-xl + X2:5 1 Xl :5 3 XI> X2 ;::: 0

(a) Solve the problem by the simplex method, where the entering variable is the nonbasic variable with the most negative z-row coefficient.

(b) Resolve the problem by the simplex algorithm, always selecting the entering variable as the nonbasic variable with the least negative z-row coefficient.

(c) Compare the number of iterations in

(a) and (b). Does the selection of the entering variable as the nonbasic variable with the most negative z-row coefficient lead to a smaller number of iterations? What conclusion can be made regarding the optimality condition?

(d) Suppose that the sense of optimization is changed to minimization by multiplying z by -1. How does this change affect the simplex iterations?