# Calculus

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 460 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue?

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1. Let n be the number of \$10 increases in rent. Total revenue = (# units)(rent)

=(80-n)(460+10n)
=36800 + 340n - 10n^2
has a max at 17

so, rent = 460-170 = 290

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2. The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 360 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue?

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