This is Section 3.8 Problem 30: A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $16 per day to maintain. (a) The demand function, expressed by p , the price in dollars charged for each room per day, as a function of x , the number of rooms occupied, is p=D(x)= where x is defined between and (b) The profit function is P(x)= where x is defined between and (c) To maximize its profit, the price the motel charges should be dollars per room per day. (Keep 2 decimal places (rounded), unless the exact answer has fewer decimal places.)