Problem 29E

29. Suppose that the cost (in dollars) for a company to produce $x$ pairs of a new line of jeans is

$$ C(x)=2000+3 x+0.01 x^{2}+0.0002 x^{3} $$

(a) Find the marginal cost function.

(b) Find $C^{\prime}(100)$ and explain its meaning. What does it predict?

(c) Compare $C^{\prime}(100)$ with the cost of manufacturing the 101 st pair of jeans.



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