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?

Question

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?

amistre64 · Answer

800 * 100 = 80000

810 * 99 = 80190

900 * 90 = 81000

1000 * 80 = 80000

(800 + 10n) (100-1n) = revenue...seems about right

amistre64 · Answer

(800 + 10(3)) (100 - 3) = (830)(97) = 80510

that look like a good equation to use :)

amistre64 · Answer

(800+10n)(100-n)

80000 +200n -10n^2

200 -20n = 0 ... n=200/20 = 20/2 = 10

lets see if it works :)

amistre64 · Answer

at a rate of $900 there will be 90 rooms filled and the total revunue is 81000
that seems to be the answer :)

amistre64 · Answer

(800 +10(11)) (100 - 11)

(910)(89) = 80990 .... so yeah, its good

anonymous · Answer

yup