The data in the table, from a survey of hotels with comparable rates on Hilton Head...

 

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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 63 134 47 143 45 149 45 154 40 194 32 The goal is to use these data to help answer the following questions. A. What price per day will maximize the daily off-season revenue for a typical hotel in this group if it has 200 rooms available? B. Suppose that for this typical hotel, the daily cost is $5510 plus 830 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 200 to get the hypothetical room occupancy. Create the revenue data points that compare the price with the revenue, R, which is equal to price times the room occupancy. 2. Find an equation that models the revenue, R, 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. 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 63 134 47 143 45 149 45 154 40 194 32 The goal is to use these data to help answer the following questions. A. What price per day will maximize the daily off-season revenue for a typical hotel in this group if it has 200 rooms available? B. Suppose that for this typical hotel, the daily cost is $5510 plus 830 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 200 to get the hypothetical room occupancy. Create the revenue data points that compare the price with the revenue, R, which is equal to price times the room occupancy. 2. Find an equation that models the revenue, R, 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.

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