anonymous
  • anonymous
The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $800 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue?
Mathematics
jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
800 * 100 = 80000 810 * 99 = 80190 900 * 90 = 81000 1000 * 80 = 80000 (800 + 10n) (100-1n) = revenue...seems about right
amistre64
  • amistre64
(800 + 10(3)) (100 - 3) = (830)(97) = 80510 that look like a good equation to use :)
amistre64
  • amistre64
(800+10n)(100-n) 80000 +200n -10n^2 200 -20n = 0 ... n=200/20 = 20/2 = 10 lets see if it works :)

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amistre64
  • amistre64
at a rate of $900 there will be 90 rooms filled and the total revunue is 81000 that seems to be the answer :)
amistre64
  • amistre64
(800 +10(11)) (100 - 11) (910)(89) = 80990 .... so yeah, its good
anonymous
  • anonymous
yup

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