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

Mathematics

Baylee Ferrell

9 December, 22:22

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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Answers (1)

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Jazlene Simon · Answer 1

Answer: to maximize profit the management must continue charging $40 per room because it will obtain a profit of $1,920 better than $1,870 if it rises the rate.

Step-by-step explanation:

Profit without the increase

60 (number of rooms) * $40 (rate per room) = $ 2,400

costs of day to service = 60 (rooms) * $8 (costs day to service) = $480

Total Profit = $2,400 - $480 = $1,920

Profit with the increase

55 (5 fewer than before) * 42 (rate with the increase) = $ 2,310

costs of day service 55 (rooms) * 8 (costs day to service) = $440

Total Profit = $2,310 - $440 = $1,870