The Hotel Florence has 550 rooms. Currently the hotel is filled . The daily rental is $ 700 per room.

Question

For every $ 14 increase in rent the demand for rooms decreases by 7 rooms.
Let x = the number of $ 14 increases that can be made.
What should x be so as to maximize the revenue of the hotel ?
What is the rent per room when the revenue is maximized? $
What is the maximum revenue? $

Answer 1

revenue is room-charge * #rooms, so
R(x) = (700+14x)(550-7x)

That's just a parabola, and you can easily find its vertex.

Answer 2

thank you