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 x apartments is represented by the following function. P(x) = -7x2 + 1550x - 54000 (a) What is the actual profit realized from renting the 41st unit, assuming that 40 units have already been rented?
$ 1     

(b) Compute the marginal profit when x = 40 and compare your results with that obtained in part (a).
$ 2 P(x) = -7x2 + 1550x - 54000 (a) What is the actual profit realized from renting the 41st unit, assuming that 40 units have already been rented?
$ 1     

(b) Compute the marginal profit when x = 40 and compare your results with that obtained in part (a).
$ 2

Explanation / Answer

P(x) = -7x2+ 1550x - 54000

a.)

dp/dx = -14x+150

40 units profit increase = -14*40+1550=990

41 units profit increase = -14*41+1550=976

then increament in profit = (990+976)/2=983

b.)

dp/dx = -14x+150

by increasing one unit profit increase = -14*40+1550=990

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