Question

An electronic manufacturing company has determined that the monthly cost of producing x units of its newest stereo is C(x) = 2500 + 10x , and the monthly demand equation for this cost function is p equals fraction numerator 60 comma 000 minus x over denominator 1500 end fraction where x is the number of units and p is the price in dollars. Use the demand equation to find the monthly revenue equation. Then find the monthly profit equation and use it to compute the monthly marginal profit for a production level of 8250 units. The monthly marginal profit when 8250 units are produced and sold is _____________ dollars

Answer 1

The monthly marginal profit when 8250 units are produced and sold is 199,625 dollars

Explanation:

C(x) = 2500 + 10x

p =(60,000 - x) /1500

Sales Revenue = Units Sold x Sales Price

Sales Revenue = x * (60,000 - x) /1500

Profit= Sales revenue - cost

Profit= p * units sold -2500 + 10x

Profit= x * ((60,000 - x) /1500 )-2500 + 10x

If x is 8250

Profit= 8250*((60,000 - 8250) /1500) -2500 + 10*8250

Profit= 51750/1500 *8250 -2500 + 82500

Profit=34.5*8250 -2500 + 82500=199625

Profit=199625

Answer 2

Answer: The monthly marginal profit when 8250 units are produced and sold is 2,427,125 dollars

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