1. ## 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 $16 increases that can be made. What should x be so as to maximize the revenue of the hotel ? _______________ What is the rent per room when the revenue is maximized?$_______________

3. ## Re: Revenue

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 "$16 increases"? The total revenue will be the number or rooms rented times the rent for each room. Once you have that "revenue function", do you know how to maximize a function? What should x be so as to maximize the revenue of the hotel ? _______________ What is the rent per room when the revenue is maximized?$_______________
What is the maximum revenue? \$_________________