February 6, 2016

Homework Help: please chech my answer optimization

Posted by julie on Sunday, November 11, 2007 at 7:57pm.

The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $400 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each $5 increase in rent. What rent should the manager charge to maximize revenue?

this is my work so far:
So i want maximize the revenue so I need an expression for the revenue.

revenue = (number of units rented) (rent per unit)

100 * $400 = $40 000

let increments be x:

The number of units rented would then be 100 - x and the rent per unit would be $400 + $5x. Hence the revenue would be

(100 - x)($400 + $5x)

Then i took the derivative of that function above to maximize it and i got x=30.

then i plugged in 30 in the revenue function and i got 4900 dollars. i don't think that right because increasing the rent from 800 to 4900 is too much.

would equation would i substitute x=30 in then?

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