Calculus-Applied Optimization Problem

The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 425 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent.

Let the rent on an apartment be x dollars per month, and let N be the number of apartments rented each month, and let R be the revenue (the gross income) brought in each month by the apartment manager.

N(x)=______apartments
R(x)=______dollars

What rent should the manager charge to maximize revenue?

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1. N(x) = 100-(x-425)/9
R(x) = x*N(x) = x(100-(x-425)/9) = 1/9 (1325x-x^2)

dR/dx = 1/9 (1325-2x)
dR/dx=0 at x=1325/2 = \$662.50

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posted by Steve

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