Consider the following problem.

Maximize Z  2x1 2x2  3x3, subject to x1  x2  x3 4 (resource 1)

2x1 x2  x3 2 (resource 2)

x1  x2  3x3 12 (resource 3)

and x1  0, x2  0, x3  0.

D,I

(a) Work through the simplex method step by step to solve the problem.

(b) Identify the shadow prices for the three resources and describe their significance.

C

(c) Use a software package based on the simplex method to solve the problem and then to generate sensitivity information. Use this information to identify the shadow price for each resource, the allowable range to stay optimal for each objective function coefficient and the allowable range to stay feasible for each right-hand side.