# Calculus

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The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 472 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue?

• Calculus -

d unit/drent= 1unit/4dollars rent.

revenue=80+x)(472-4x)

drevenue/dx=-4(80+x) + (472-4x)=0
240+4x-472=-4x
8x=232
x=29 units, so rent should be 472-4*29

check that.

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