Consider the following problem.

Minimize Z  2x1  3x2  x3, subject to x1  4x2  2x3  8 3x1  2x2  2x3  6 and x1  0, x2  0, x3  0.

(a) Reformulate this problem to fit our standard form for a linear programming model presented in Sec. 3.2.

I

(b) Using the Big M method, work through the simplex method step by step to solve the problem.

I

(c) Using the two-phase method, work through the simplex method step by step to solve the problem.

(d) Compare the sequence of BF solutions obtained in parts (b)

and (c). Which of these solutions are feasible only for the artificial problem obtained by introducing artificial variables and which are actually feasible for the real problem?

C

(e) Use a software package based on the simplex method to solve the problem.