# Revenue

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• Oct 2nd 2012, 06:02 AM
spyder12
Revenue
The Hotel Summerfield has 500 rooms. Currently the hotel is filled . The daily rental is \$ 850 per room.
For every \$ 16 increase in rent the demand for rooms decreases by 8 rooms.
Let x = the number of \$ 16 increases that can be made.
What should x be so as to maximize the revenue of the hotel ? _______________
What is the rent per room when the revenue is maximized? \$_______________
What is the maximum revenue? \$_________________
• Oct 2nd 2012, 10:02 AM
MaxJasper
Re: Revenue
\$925 a night looks better!
• Oct 2nd 2012, 12:38 PM
HallsofIvy
Re: Revenue
Quote:

Originally Posted by spyder12
The Hotel Summerfield has 500 rooms. Currently the hotel is filled . The daily rental is \$ 850 per room.
For every \$ 16 increase in rent the demand for rooms decreases by 8 rooms.
Let x = the number of \$ 16 increases that can be made.

If each room cost \$850 (I'm not going to be staying there!) to start with, and there are x "\$16 increases", what would the price per room be?
If they initially rented all 500 rooms and the number of rooms decreased by 8 for each \$16 increase, how many rooms will be rented with x "\$16 increases"? The total revenue will be the number or rooms rented times the rent for each room.

Once you have that "revenue function", do you know how to maximize a function?

Quote:

What should x be so as to maximize the revenue of the hotel ? _______________
What is the rent per room when the revenue is maximized? \$_______________
What is the maximum revenue? \$_________________