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

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The data in the table, from a survey of resort hotels withcomparable rates on Hilton Head Island, show that room occupancyduring the off-season (November through February) is related to theprice charged for a basic room.
Price per Day $ Occupancy Rate %
104 53
134 47
143 46
149 45
164 40
194 32
First make a linear equation using linear regression on yourcalculator where x = price and y = occupancy rate.
Convert occupancy rate to quantity of rooms in a 200-roomhotel.
Write down a revenue function for a 200-room hotel.
What price per day will maximize the daily off-season revenuefor a typical 200-room hotel? Use Calculus to determine themaximum.
If this 200-room hotel has daily operating costs of $5510 plus$30 per occupied room. What price will maximize the daily profitduring the off-season? Again use calculus to determine themaximum
More detailed instructions are given on page 690 of the textbook(12th edition).

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4.3 Ratings (927 Votes)

Solution Backup Theory The linear regression model Y 0 1X 1 where is the error term which is assumed to be Normally distributed with mean 0 and variance 2 Estimated Regression of Y on X is given by Ycap 0cap 1capX 2 where 1cap SxySxx and 0cap Ybar 1capXbar3 Mean X Xbar 1nsum of xi 4 Mean Y Ybar 1nsum of yi 5 Sxx sum See Answer

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