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.
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