# calculus

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The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 350 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. What rent should the manager charge to maximize revenue?

• calculus -

I'll start you off ....

let the number of \$7 increases be n
then number rented = 100 - n
rent charged = 350 + 7n

Revenue = (100-n)(350+7n)

expand, take the derivative, set that equal to zero and solve for n.

• calculus -

bah

• calculus -

25

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