1. ## revenue/profit problem

You manage a 280 unit motel. All units will be occupied, on average, when
you charge $50/per day per unit. Experience shows that for each$1 per day per unit that you increase the price, you will accrue 2 vacancies. Each occupied room costs $4 a day to clean and supply. On this basis, what price, in dollars, should you charge per unit per day to maximize your profit? 2. Hello, Originally Posted by gumi You manage a 280 unit motel. All units will be occupied, on average, when you charge$50/per day per unit. Experience shows that for each $1 per day per unit that you increase the price, you will accrue 2 vacancies. Each occupied room costs$4 a day to clean and supply. On this basis, what price, in dollars, should you charge per unit per day to maximize your profit?
Let X the number $1 you add to the original price. The price per day & per unit is 50+X. The profit of each occupied room is (50+X)-4=46+X, where 4 is the cost for cleaning and supplying. So the number of occupied rooms is 280-2X (each time you increase of 1$, there are 2 vacancies).
We assume that an empty room makes no profit.

Therefore, the total profit is P(X)=(46+X)(280-2X)=-2X²+188X+12880.
We want it to be maximum.

--> $P'(X)=-4X+188$, which annulates at X=188/4=47.

So the price of the rooms has to be 50+47=97.

I hope I didn't make any mistake