Question concerning :Marginal cost, Revenue and Profit....?

Question

The total cost (in dollars) of producing x coffee machines is

C(x)=2500+60x-0.4x^2

(A)Find the exact cost of producing the 21st machine.
Exact cost of 21st machine =

(B)Use marginal cost to approximate the cost of producing the 21st machine.
Approx. cost of 21st machine =

Answer 1

(A) Exact cost of of producing 21st machine = Cost of 21 machines - Cost of 20 machines
= (2500+60*21-0.4*(21^2)) - (2500+60*20-0.4*(20^2))
= 60 - 0.4*(41*1) = 60 - 16.4 = 43.6.

(B) Marginal Cost MC = (d/dx)C(x) = 60 - 0.4*2*x = 60 -0.8*x
Approx. Cost of producing 21st machine = 60 - 0.8*20 = 44.
Note that here x=20 because marginal cost of producing 21st machine is calculated after the 20th machine has been produced.

Answer 2

The cost of producing 20 coffee machines is C(20); the cost of producing 21 coffee machines is C(21). So the cost of producing that 21st coffee machine is C(21) - C(20) (I leave its calculation to you).

The marginal cost is C'(20), which is $44.00

Answer 3

The profit maximizing quantity of output occurs where marginal cost = marginal revenue (i.e., where the cost of producing another unit = the revenue you can get from having produced it). If fixed costs are increased, the average cost increases, but the marginal cost (cost per additional unit) is unchanged. Since neither marginal cost nor marginal revenue are affected, there will be no change in the profit maximizing quantity of output produced.