The total cost​ (in dollars) of producing x food processors is ​C(x)=2100+80x−0.5x^2.

Question

The total cost​ (in dollars) of producing x food processors is ​C(x)=2100+80x−0.5x^2.

​(A) Find the exact cost of producing the 41st food processor.

​(B) Use the marginal cost to approximate the cost of producing the 41st food processor.

Answer 1

(A) C(41) - C(40) = (2100 + 80·41 - 0.5·41²) - (2100 + 80· 40 - 0.5·40²) = $39.50 to produce 41st item

(B) C'(x) = 80 - x; C'(40) = 80 - 40 = $40 per item

So exact cost to produce 41st item approximatly equel marginal cost of producing 40 item.