Consider the following problem.

Maximize Z  90x1  70x2, subject to 2x1  x2 2 x1 x2  2 and x1  0, x2  0.

(a) Demonstrate graphically that this problem has no feasible solutions.

C

(b) Use a computer package based on the simplex method to determine that the problem has no feasible solutions.

I

(c) Using the Big M method, work through the simplex method step by step to demonstrate that the problem has no feasible solutions.

I

(d) Repeat part

(c) when using phase 1 of the two-phase method.

ough the simplex method step by step to solve the problem.
I

(c) Using the two-phase method, construct the complete first simplex tableau for phase 1 and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable.
I

(d) Work through phase 1 step by step.

(e) Construct the complete first simplex tableau for phase 2.
I

(f) Work through phase 2 step by step to solve the problem.
(g) Compare the sequence of BF solutions obtained in part

(b) with that in parts

(d) and ( f ). 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 (h) Use a software package based on the simplex method to solve the problem.