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Question

Marginal Cost

 The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function.

C(x) = 2000 + 2x − 0.0001x²    (0 ≤ x ≤ 6000)

(a)

What is the actual cost incurred in producing the 1061st and the 2051st disc? (Round your answers to the nearest cent.)

1061st disc. $ 

2051st disc. $  

(b)

What is the marginal cost when x = 1060 and 2050? (Round your answers to the nearest cent.)

1060. $ 

2050. $  

Answer 1

(a) C₁₀₆₁ = C(1061) - C(1060) = 4009.43 - 4007.64 = $1.79

C₂₀₅₁ = C(2051) - C(2050) = 5681.34 - 5679.75 = $1.59

(b) Marginal cost C'(x) = 2 - 0.0002x;

C'(1060) = 2 - 0.0002·1060 = $1.79 ≈ C₁₀₆₁

C'(2050) = 2 - 0.0002·2050 = $1.59 ≈ C₂₀₅₀^