suppose that on a saturday night at 10pm a large hotel has 300 vacant rooms, with little expectation of renting them at such a late hour on a weekend. a traveler comes in the door, looking a bit down on his luck, and asks how much a room will cost. since he can't afford the normal rate of $150, the night manager decides to let him stay in the room for only $40. is it likely that this decision reduced, or increased, the hotel's profits? explain your answer.