The manager of a large apartment complex knows from experience that 90 units wil

Question

The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 500 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?

Explanation / Answer

We have the point (500, 90). Demand = -.1x + b, where x is price => 90 = -.1(500) + b => b = 90 + .1(500) = 90 + 50 = 140 Demand = -.1x + 140 Revenue = x*Demand = -.1x^2 + 140x Revenue' = -.2x + 140 0 = -.2x + 140 => .2x = 140 => x = 700 So the manager should charge $700 to maximize revenue.

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