Suppose that an optimization model in decision variables w1 and w2 has constraints 5w1 + 2w2 ≤ 10, w2 ≥ 0.
1. Devise a maximizing linear objective function for which the model has a unique optimal solution and demonstrate that fact by solving the model graphically.
2. Devise a maximizing linear objective function for which the model has multiple optimal solutions and demonstrate that fact by solving the model graphically.
3. Devise a maximizing linear objective function for which the model is unbounded and demonstrate that fact by solving the model graphically.