Question

The total cost (in dollars) of producing x food processors is C(x) = 2000 + 90x-0 2x2
(A) Find the exact cost of producing the 91st food processor.
(B) Use the marginal cost to approximate the cost of producing the 91st food processor.
(A) The exact cost of producing the 91st food processor ​

Answer 1

Answer:

10

Step-by-step explanation:

Answer 2

Answer :-

(A)

→ C(x) = 2000 + 90x - 0.2x²

→ C(91) = 2000 + 90*91 - 0.2(91)² = 2000 + 8190 - 1656.2 = 8533.8

and,

→ C(90) = 2000 + 90*90 - 0.2(90)² = 2000 + 8100 - 1620 = 8480 .

so,

→ The exact cost of producing the 91st food processor = C(91) - C(90) = 8533.8 - 8480 = $53.8 (Ans.)

(B)

→ C(x) = 2000 + 90x - 0.2x²

→ Marginal cost , C'(x) = 90 - 0.4x .

so,

→ C'(90) = 90 - 0.4*90 = 90 - 36 = $54 (Ans.)