Posted by Z32 on Monday, June 22, 2009 at 12:58am.
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 370 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 5 dollar increase in rent. Similarly, one additional unit will be occupied for each 5 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Calculus  Reiny, Monday, June 22, 2009 at 9:06am
let the number of $5 increases by n
(e.g. if n=1 rent will be 375, if n = 4 rent will be 390 etc)
so the rent will be $(370+5n)
number of units occupied will be 90  n
Revenue = (370+5n)(90n)
expand and simplify, take the first derivative, set that equal to zero and solve for n
I did not finish it, but if n is positive there will be an increase in rent and a decrease in the number of units rented.
If n should turn out negative, there would be a decrease in the rent and an increase in the number of units rented.

Calculus  Anonymous, Saturday, October 27, 2012 at 12:48am
No one on this whole site has this question answered correctly..

Calculus  Anonymous, Thursday, November 20, 2014 at 11:20am
The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 300 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 2 dollar increase in rent. Similarly, one additional unit will be occupied for each 2 dollar decrease in rent. What rent should the manager charge to maximize revenue?
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