Question

Gritz-Charlston is a 300-unit luxury hotel. All rooms are occupied when the hotel charges $80 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $22 per day to service and maintain. What should the hotel charge per day in order to maximize profit?

Answer 1

Answer:

The hotel should charge $201 per day in order to maximize profit

Explanation:

According to the given data we have the following:

The number of occupied rooms is 300-x, and x vacant rooms.

Hence, The revenue R(x) = (300-x) * ($80 + x), the number of occupiedrooms times the charge per room.

The cost C(x) = (300-x) * $22.

Therefore, The profit P(x) = R(x)-C(x) = (300-x) (58 + x) = 17400 + 242 x -x^2.

P'(x) = 242 - 2x.

Critical point: x= 121.

So Charge = $80 + x = $80 + $121 = $201

The hotel should charge $201 per day in order to maximize profit