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) = [tex]\frac{d}{dx}(-11x^{2}+1804x-43000)[/tex]
= -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.
