# Calculus

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?

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1. 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)(90-n)

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.

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2. No one on this whole site has this question answered correctly..

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3. 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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4. 344

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