An apartment complex contains 130 units. Records show that there isan average of
ID: 3091063 • Letter: A
Question
An apartment complex contains 130 units. Records show that there isan average of 20 unoccupied units when the rent is set at $240.00per month, and that for each $2.00 reduction in the monthly rent,one additional unit can be filled. Under these conditions whatmonthly rent will yield the greatest revenue?This question actually involves using calculus, in thiscase I need to find the derivative of the revenue function. Butfirst, I must find the original revenue function.
I've attempted the question several times, the closest Igot to being right is this:
R(x) = ( 240 -2x)(20 + x) which then of course turnsinto R(x) = -2x^2 + 200x + 4800. I asked my professor andshe told me my revenue function isincorrect.
Any help would be greatly appreciated!
This question actually involves using calculus, in thiscase I need to find the derivative of the revenue function. Butfirst, I must find the original revenue function.
I've attempted the question several times, the closest Igot to being right is this:
R(x) = ( 240 -2x)(20 + x) which then of course turnsinto R(x) = -2x^2 + 200x + 4800. I asked my professor andshe told me my revenue function isincorrect.
Any help would be greatly appreciated!
Explanation / Answer
R(x) = (240 - 2x)(130-(20-x)) at 240 per month, there's an average of 20 unoccupied units, so therevenue = 240 * 110 for each $2 reduction, one additional unit can be filled, so therevenue =(240 -2(1)) (130 -20 +1)