The manager of a large apartment complex knows from experience that 90 units wil
ID: 2859636 • Letter: T
Question
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 320 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue? Note: Revenue is the total amount of money brought in; in this problem it is equal to the rent per apartment times the number of apartments rented.
Explanation / Answer
R(x) = (320-4x)(90+x) or
R(x) = (320+4x)(90-x).
let's choose R(x) = (320-4x)(90+x)
Minima-Maxima concept, we set R'(x) = 0
we get: R'(x) = 0 = 320-4x = 360 +4x
8x = 40
x = 5
:
we get: R(x) = (320-4(5)(90+5)
=(320-20)(95)
= 300(95)
R(x) = 28500 dollars
Rent should be 300 dollars
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