Consider the following problem.

Maximize Z c1x1  c2x2, subject to 2x1  x2 b1 x1  x2 b2 and x1  0, x2  0.

Let x3 and x4 denote the slack variables for the respective functional constraints. When c1 3, c2 2, b1 30, and b2 10, the simplex method yields the following final simplex tableau.

(a) Use graphical analysis to determine the allowable range to stay optimal for c1 and c2.

(b) Use algebraic analysis to derive and verify your answers in part (a).

(c) Use graphical analysis to determine the allowable range to stay feasible for b1 and b2.

(d) Use algebraic analysis to derive and verify your answers in part (c)

C

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