A 440-unit hotel is trying to determine their daily rates. From experience, the hotel manager knows that all rooms are typically occupied when the daily room rate is $92. Market research indicates that for every increase of x

Question

dollars in the daily room rate, there will be 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

p = (440 - x) (92 - 22 + x) = (440 * 70) + 370 x - x^2

the max is on the axis of symmetry
... x = -b / 2a = -370 / -2 = 185

rate for max profit ... 92 + 185