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. P(x) = -11 x^2 + 1804 x - 43,000 To maximize the monthly rental profit, how many units should be rented out?
units What is the maximum monthly profit realizable? $

Answer 1

Answer:

82 apartments should be rented.

Maximum profit realized will be $30964.

Step-by-step explanation:

Monthly profit realized from renting out x apartments is modeled by

P(x) = -11x² + 1804x - 43000

To maximize the profit we will take the derivative of the function P(x) with respect to x and equate it to zero.

P'(x) = $\frac{d}{dx}(-11x^{2}+1804x-43000)$

       = -22x + 1804

For P'(x) = 0,

-22x + 1804 = 0

22x = 1804

x = 82

Now we will take second derivative,

P"(x) = -22

(-) negative value of second derivative confirms that profit will be maximum if 82 apartments are rented.

For maximum profit,

P(82) = -11(82)² + 1804(82) - 43000

        = -73964 + 147928 - 43000

        = $30964

Therefore, maximum monthly profit will be $30964.