2. A university's administrators have determined that their students fall into two categories as far as room and board demand is concerned, whom they call Eaters and Sleepers. Sleepers are willing to pay up to 5,500 for a dorm room, and 2,500 for a meal plan. Eaters are willing to pay up to 3,000 for a dorm room, and 6,000 for a meal plan. There are equal numbers of each type of student. (a) What prices should the university charge when they charge separate prices for dorm rooms and meal plans, if the goal is to maximize revenue? (b) Suppose the university decides to only offer the bundle. What price should it charge, assuming that its goal is to maximize revenue. Could it do better using a mixed bundling pricing strategy? (c) How would your answers to parts (a) and (b) change, if at all, if you were told that it cost 2,000 per student to provide meal plans, and that the goal is to maximize profits? (Assume that dorm rooms are already built, and all their costs are sunk.) Explain your reasoning