A 60 room hotel is filled to capacity every night at a rate of​ $40 per room. The management wants to determine if a rate increase would increase their profit. They are not interested in a rate decrease. Suppose management determines that for each​ $2 increase in the nightly​ rate, five fewer rooms will be rented. If each rented room costs​ $8 a day to​ service, how much should the management charge per room to maximize​ profit?

Question

A 60 room hotel is filled to capacity every night at a rate of​ $40 per room.

The management wants to determine if a rate increase would increase their profit. They are not interested in a rate decrease. Suppose management determines that for each​ $2 increase in the nightly​ rate, five fewer rooms will be rented. If each rented room costs​ $8 a day to​ service, how much should the management charge per room to maximize​ profit?

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