Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function. P(x) = -2x2 + 1700x - 43000 (a) What is the actual profit realized from renting the 41st unit, assuming that 40 units have already been rented?

Answer:From renting the 41st unit, you have made an actual profit of 1538 dollars.Step-by-step explanation:The problem states that the monthly profit (in dollars) realized from renting x apartments is represented by the following function.[tex]P(x) = -2x^{2} + 1700x - 43000[/tex]This mean that when you have rented x apartments, you have made a profit of P(x) dollars.(a) What is the actual profit realized from renting the 41st unit, assuming that 40 units have already been rented?After you have rented 40 apartments, you have made a profit of P(40) dollars.After you have rented 41 apartments, you have made a profit of P(41) dollars.To find the actual profit from renting the 41st unit, you have to calculate P(41) - P(40).So[tex]P(x) = -2x^{2} + 1700x - 43000[/tex][tex]P(40) = -2(40)^{2} + 1700(40) - 43000 = 21800[/tex][tex]P(41) = -2(41)^{2} + 1700(41) - 43000 = 23338[/tex]So[tex]P(41) - P(40) = 23338 - 21800 = 1538[/tex]From renting the 41st unit, you have made an actual profit of 1538 dollars.