Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly prof

Question

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function.

To maximize the monthly rental profit, how many units should be rented out?
units

What is the maximum monthly profit realizable?
$

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. P(x) = -10x 2 + 1760x - 45,000 To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?

Explanation / Answer

The max will be when dP/dx = 0

dP/dx = -22x^2 + 1936 = 0
x^2 = 1936/22 = 88

So 88 units need to be rented out to maximize profits.

Just plug x = 88 into the eqution for P to get the actual profit.
P = -11(88)^2 + 1936(88) - 46000
P = 209552 dollars

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