A real estate office handles 50 apartment units. When the rent is $720 per month, all units are occupied. However, on the averag

Question

3 years ago

12

A real estate office handles 50 apartment units. When the rent is $720 per month, all units are occupied. However, on the averag

e, for each $40 increase in rent, one unit becomes vacant. Each occupied unit requires an average of $48 per month for service and repairs. What rent should be charged to obtain a maximum profit?

Mathematics

1 answer:

Elena L [17] · Answer 1 · 2022-03-11T21:50:38+03:00

Elena L [17]3 years ago

3 0

If n is the number of apartments are occupied. Total Rent company is getting: $(720 + 40(50-n)) n - 48n$ 

We have to maximize the above equation.

$y=720n + 2000n - 40n^2 - 48n
\\y=2672n-40n^2
\\y'=(2672n-40n^2)'=2672-80n
\\y'=0
\\2672-80n=0
\\2672=80n
\\n= 33.4 \approx 33$

 $\text{Rent} = 720 + (50-33)40 = 720 + 680 = \$1400$