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

income

= (940+25n)(218-5n)

= 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( (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

or

the x of the vertex is -b/(2a) = -750/-250 = 3

for 3 increases.

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