Suppose that the following constraints have been provided for a linear programming model.

x1  3x2  30

3x1  x2  30 and x1  0, x2  0.

(a) Demonstrate 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?