Answer: The monthly marginal profit when 8250 units are produced and sold is 2,427,125 dollars
Step-by-step explanation:
C(x) = 2500 + 10x
D(x) = 60000 - x/1500
Use the demand equation to find the monthly revenue equation.
R(x) = x.D(x) = x(60000 - x/1500) = 60000x - x²/1500
Find the monthly profit equation
P(x) = R(x) - C(x) = 60000x - x²/1500 - (2500 + 10x) =
60000x - x²/1500 - 2500 - 10x = 60000x - x² - 3750000 - 15000x/1500 =
45000x - x² - 3750000/1500
use it to compute the monthly marginal profit for a production level of 8250 units
P(8250) = 45000*8250 - 8250² - 3750000/1500 = 2,427,125
The monthly marginal profit when 8250 units are produced and sold is 2,427,125 dollars
