Suppose that the following constraints have been provided for a linear programming model with decision variables x1 and x2.

x1  3x2 30 3x1  x2 30 and x1  0, x2  0.

(a) Demonstrate graphically that the feasible region is unbounded.

(b) If the objective is to maximize Z  x1  x2, does the model have an optimal solution? If so, find it. If not, explain why not.

(c) Repeat part

(b) when the objective is to maximize Z  x1 x2.

(d) For objective functions where this model has no optimal solution, does this mean that there are no good solutions according to the model? Explain. What probably went wrong when formulating the model?

D,I

(e) Select an objective function for which this model has no optimal solution. Then work through the simplex method step by step to demonstrate that Z is unbounded.

C

(f) For the objective function selected in part (e), use a software package based on the simplex method to determine that Z is unbounded.