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A motel owner observes that when a room is priced at $120 per day, all 200...

A motel owner observes that when a room is priced at $120 per day, all 200 rooms of the motel are occupied. For every $10 rise in the charge per room per day, 5 rooms are vacant. Each occupied room costs an additional $38 per day to maintain.
(a) Find the profit function.
(b) Find the price of per room per day the motel should charge in order to maximize its
profit.
(c) How many room is occupied to have the maximum profit? (d) What would be the maximum profit of the motel?

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