Posted by Anonymous on Sunday, January 26, 2014 at 7:47pm.
A real estate company owns 218 efficiency apartments, which are fully occupied when the rent is $940 /month. The company estimated that for each $25 increase in rent, 5 apartments will become unoccupied. What rent should be charged so that the company will receive the maximum monthly income?
- Math - Reiny, Sunday, January 26, 2014 at 8:14pm
let the number of $25 increases be n
rent = 940 + 25n
number rented = 218-5n
= 204920 +750n - 125n^2
If you know Calculus:
d(income) = 750 - 250n = 0 for a max of income
n = 3
if you don't know Calc
complete the square:
-125(n^2 - 6n + 9 - 9) + 204920
= -125( (n-3)^2 - 9) + 204920
= -125(n-3)^2 + 1125 + 204920
= -125(n-3)^2 + 206045
vertex is (3, 206045)
there should be 3 increases for a rent of 940+75 = 1015
the x of the vertex is -b/(2a) = -750/-250 = 3
for 3 increases.
Answer this Question
- optimization calculus - a real estate office manages 50 apartments in downtown ...
- Calculus - A real estate office manages 50 apartments in a downtown building. ...
- Calculus-Applied Optimization Problem - The manager of a large apartment complex...
- Probabilities - An apartment building has 140 apartments, all renting at the ...
- Statistics - The mean monthly rent for a one-bedroom apartment without a doorman...
- Probability & Statistics - You want to rent an unfurnished one-bedroom apartment...
- economics - If departing tenants sell access to rent-controlled apartments, whi ...
- statistics - David wants to rent an unfurnished apartment for next semester. He ...
- Stats - You want to rent an unfurnished one-bedroom apartment in Boston next ...
- Math 1200 - a complex has 205 apartment units. When the rent is $635 per month ...