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: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 - 43000To 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 + 1804For P'(x) = 0,-22x + 1804 = 022x = 1804x = 82Now 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         = $30964Therefore, maximum monthly profit will be $30964.