Pr8attymaris
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The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 496 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Verified Answer :

HomertheGenius

R - total revenue
Revenue without changing the rent:
R = $496 · 90 = $44,640
x - number of dollars increased
R = ( 90 - x/8 ) ( 496 + x )
R = - x²/8 + 28 x + 44,640
R` = - x/4 + 28
- x/4 + 28 = 0
x/4 = 28
x = 28 · 4 = $112
Maximum revenue: R = 112 · 76 = $46,208
The rent should be:
$112 + $496 = $608 per month

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