The marginal cost function is C'(x) = 4 + 0.06x + 0.0009x². The cost of 150th pair of jeans is $13.135. The actual cost of 151st pairs jeans is $13.1359.
The cost of the pair of jeans is defined by the function,
C(x) = 2000 + 4x + 0.03x² + 0.0003x³
a. Marginal cost function is,
Differentiating with respect to x,
C'(x) = 4 + 0.06x + 0.0009x²
b. The value of C'(150),
Putting x = 150,
C'(150) = 4 + 0.06(150) + 0.0009(150)
C'(150) = 4 +9 + 0.135
C'(150) = $13.135.
It predicts the cost of 150th pair of jeans.
c. The cost of 151st pair is,
C(151) = 4 + 0.06(151) + 0.0009(151)
C(151) = 4 + 9.06 + 0.1359
C(151) = $13.1359.
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