II. Room Pricing in the Off-Season (Modeling)
The data in the table, from a survey of hotels with comparable rates on Hilton Head Island, show that room occupancy during the off-season (November through February) is related to the price charged for a basic room.
The goal is to use these data to help answer the fol-lowing questions.
What price per day will maximize the daily offseason revenue for a typical hotel in this group if it has 200 rooms available?
Suppose that for this typical hotel, the daily cost is $5510 plus $30 per occupied room. What price will maximize the profit for this hotel in the off-season?
The price per day that will maximize the off-season profit for this typical hotel applies to this group of hotels. To find the room price per day that will maximize the daily revenue and the room price per day that will maximize the profit for this hotel (and thus the group of hotels) in the off-season, complete the following.
Find an equation that models the revenue, R, as a function of the price per day, x.
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