Consider the following problem.

Maximize Z 3x1  x2  2x3, subject to x1  x2  2x3 20 2x1  x2  x3 10 and x1  0, x2  0, x3  0.

Let x4 and x5 denote the slack variables for the respective functional constraints. After we apply the simplex method, the final simplex tableau is

(a) Perform sensitivity analysis to determine which of the 11 parameters of the model are sensitive parameters in the sense that any change in just that parameter’s value will change the optimal solution.

(b) Use algebraic analysis to find the allowable range to stay optimal for each cj.

(c) Use algebraic analysis to find the allowable range to stay feasible for each bi.

C

(d) Use a software package based on the simplex method to find these allowable ranges.