Consider the following problem.

Maximize Z  5x1  4x2 x3  3x4, subject to 3x1  2x2 3x3  x4 24 (resource 1)

3x1  3x2  x3  3x4 36 (resource 2)

and x1  0, x2  0, x3  0, x4  0.
D,I

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

(b) Identify the shadow prices for the two 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.
4.9.1. Use the interior-point algorithm in your OR Courseware to solve the model in Prob.