Posted by Anonymous on Friday, October 28, 2011 at 1:10pm.
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?

Calculus  Steve, Friday, October 28, 2011 at 3:48pm
Let n be the number of $10 increases in rent. Total revenue = (# units)(rent)
=(80n)(460+10n)
=36800 + 340n  10n^2
has a max at 17
so, rent = 460170 = 290

Calculus  Anonymous, Thursday, November 17, 2011 at 7:29pm
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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