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 $15 per day to maintain. a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.
b) Find the profit function P(x).
c) Find the price of per room per day the motel should charge in order to maximize its profit.