Question

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 372 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

@Here_to_Help15

Answer 2

@Hero

Answer 3

@brianayala

Answer 4

did u already try to solve it?

Answer 5

What are the answer choices?

Answer 6

@Prototype93

Answer 7

no answer choices

Answer 8

the only thing i dont get is the last part where it says..one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. DO YOU GET IT??

Answer 9

its basically asking if he raises 6 dollars or decreases 6 dollars, will he reach maximum revenue

Answer 10

@brianayala

Answer 11

The total revenue will be given by\[R(x)=(no. units) \times (rent/unit)\]We're told that the number of units decreases by 1 for every $8 increase; i.e. for 8 x $1, or\[(no. units) = (90-\frac{x}{8})\](note when x=8 (the NUMBER of dollars increased), the number of units falls by 1)

Answer 12

@TwinYang so what would the answer be?

Answer 13

number of units decreases by 1 for every $6 increase (not $8 increase)

Answer 14

The rent should be \[$496+$112=?\]per month

Answer 15

I end up with 142R- (R^2)/6

Answer 16

@aum i just don't know what to do from there

Answer 17

Let R be the rent. Assume first R > 372
The rent exceeds 372 by (R-372)
Number of vacant units due to the higher rent = (R-372) / 6
Number of units rented = 80 - (R-372) / 6 = (480 - R + 372)/6 = (852-R)/6
Total rent revenue = R * { (852-R) / 6 } = 1/6 * R * (852-R)
Maximize Revenue

Answer 18

and the answer is? @aum

Answer 19

i am getting 400

Answer 20

Can't give out answers.

Maximize 1/6 * R * (852-R) = 1/6 * (-R^2 + 852R)
It is a parabola. Maximum occurs at the vertex.
The x-coordinate of the vertex for ax^2 + bx + c occurs at x = -b/2a

Answer 21

is 426 the corrct answer?

Answer 22

That is what I am getting.

Answer 23

yeah i got the same thing

Answer 24

and it is correct!

Answer 25

thanks

Answer 26

Alright. You are welcome.