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?

Question

Mathematics

Haiden Ramsey

10 June, 19:17

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?

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Answers (1)

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Maddison · Answer 1

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