The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximized, where x1 and x2 represent the level of the two activities.
Label each of the following statements as True or False, and then justify your answer based on the graphical method. In each case, give an example of an objective function that illustrates your answer.
a. If (3, 3) produces a larger value of the objective function than (0, 2) and (6, 3), then (3, 3) must be an optimal solution.
b. If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0, 2) or (6, 3) must also be an optimal solution.
c. The point (0, 0) cannot be an optimal solution.