The manager of a large apartment complex knows from experience that 100 units wi

Question

The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 360 dollars per month. A market survey suggests that, on the 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. Give an expression for the montly revenue in terms of x, the monthly rent being charged.

Explanation / Answer

x = monthly rent being charged per unit u = units occupied then dx/du = -9 =>x = -9*u + c at u=100, x = 360 => c = 1260 => x = -9*u + 1260 => u = (1260-x)/9 Monthly revenue = x*u = x*(1260-x)/9

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