# math

The Hotel Regal has 500 rooms. Currently the hotel is filled. The daily rental is \$ 400 per room.
For every \$4 increase in rent the demand for rooms decreases by 8 rooms.
Let x be the number of rooms that are being rented in the hotel.
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?

1. 👍 0
2. 👎 0
3. 👁 139
1. x</= 500
room rent = r = 400 + i
x = 500 - (8/4)i
cash = [ 500 - (8/4)i ] [400 +i]

cash = c = (500-2i)(400+i)
c = 20,000 - 300 i - 2i^2
dc/di = 0 for max or min = -300 - 4 i
d^2c/di^2 = -4 so max
i = -300/4 = -75 for max
x = 500 -2(-75) = more rooms than we have
so we can not make more money by going up on the rent
rent = 400 per room
cash = 400 * 500 = \$20,000

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### Math

The Hotel Regal has 600 rooms. Currently the hotel is filled . The daily rental is \$ 250 per room. For every \$ 4 increase in rent the demand for rooms decreases by 4 rooms. Let x = the number of \$ 4 increases that can be made.

asked by Irina on September 22, 2014
2. ### precalculus

The Hotel Thomasina has 500 rooms. Currently the hotel is filled . The daily rental is \$ 1000 per room. For every \$ 4 increase in rent the demand for rooms decreases by 8 rooms. Let x = the number of \$ 4 increases that can be

asked by kanchi on December 19, 2014
3. ### Pre-Calculus

The Hotel Bellville has 400 rooms. Currently the hotel is filled . The daily rental is \$ 250 per room. For every \$ 14 increase in rent the demand for rooms decreases by 5 rooms. Let x = the number of \$ 14 increases that can be

asked by Ann on October 6, 2013
4. ### pre-calculus

The Hotel Florence has 550 rooms. Currently the hotel is filled . The daily rental is \$ 700 per room. For every \$ 14 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of \$ 14 increases that can be

asked by Irina on October 13, 2014
5. ### math

Help please >.< The Hotel Lakewell has 450 rooms. Currently the hotel is filled . The daily rental is \$ 750 per room. For every \$ 4 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of \$ 4 increases

asked by Clara on February 9, 2014
6. ### Pre-Calculus

The Hotel Ventor has 400 rooms. Currently the hotel is filled. The daily rental is \$ 600 per room. For every \$6 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of \$ 6 increases that can be made. What

asked by Ann on October 14, 2013
7. ### BUSSINESS STATISTICS

Consider the average available for all hotel rooms from the previous assignment. Identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and Interpret a 95% confidence

asked by JULIET on May 6, 2012
8. ### statistics

Consider the average available for all hotel rooms from the previous assignment. Identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and Interpret a 95% confidence

asked by tom on August 2, 2011
9. ### math

1. A hotel has 120 rooms. If the number of double room is 8 more than three times the number of single rooms, how many single rooms does the hotel have? 2. A mechanic earns \$5 more per hour than his helper. On a six-hour job the

asked by gary on July 9, 2013
10. ### English

I don't know why but my previous post has been posted twice. The word cockerel is mispelt. I'd like to add the following sentences. Thank you. 1)On our holiday, we stayed in a 5-star-hotel for four days. The hotel was luxurious,

asked by Mike1 on April 11, 2011

More Similar Questions