If the objective is to maximize z -x1 x2 does the model

Question

Question: 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?