# Calculus/Optimisation

A real estate manages 80 apartment units. When the rent of each unit is \$180 per month, all units are occupied. However, for each \$6 increase in rent, one of the units becomes vacant. Each occupied unit requires an average of \$18 per month for service and repairs. What rent should be charged to realize the most profit?

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1. number of \$6 increases ---- n

right now:
number rented = 80
rent = 180

after increase:
rent = 180+6n
number rented = 80-n

revenue = (180+6n)(80-n) - 18(80-n)
=14400 + 300n - 6n^2 - 1440 + 18n
= -6n^2 + 318n + 12960
= -6(n^2 - 53n - 2160)

d(revenue)/dn = -6(2n - 53) = 0 for a max of revenue
n = 53/2

.....was expecting a whole number, check if typed correctly.

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posted by Reiny
2. Yes the question is typed correctly but thank you!

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posted by Monica

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