Question

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.

Price per Day	Occupancy Rate, %
104	53
134	47
143	46
149	45
164	40
194	32

The goal is to use these data to help answer the following questions.

1. What price per day will maximize the daily off-season revenue for a typical hotel in this group if it has  rooms available?

2. Suppose that for this typical hotel, the daily cost is  plus  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.

1. Multiply each occupancy rate by  to get the hypothetical room occupancy. Create the revenue data points that compare the price with the revenue, , which is equal to price times the room occupancy.

2. Find an equation that models the revenue, , as a function of the price per day, .

3. Use maximization techniques to find the price that these hotels should charge to maximize the daily revenue.

4. Find a model for the occupancy as a function of the price, and use the occupancy function to create a daily cost function.

5. Form the profit function.

6. Use maximization techniques to find the price that will maximize the profit.

Answer 1