Math
posted by Anonymous on .
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?

let the number of $25 increases be n
rent = 940 + 25n
number rented = 2185n
income
= (940+25n)(2185n)
= 204920 +750n  125n^2
If you know Calculus:
d(income) = 750  250n = 0 for a max of income
250n=750
n = 3
if you don't know Calc
complete the square:
125(n^2  6n + 9  9) + 204920
= 125( (n3)^2  9) + 204920
= 125(n3)^2 + 1125 + 204920
= 125(n3)^2 + 206045
vertex is (3, 206045)
there should be 3 increases for a rent of 940+75 = 1015
or
the x of the vertex is b/(2a) = 750/250 = 3
for 3 increases.