Suppose that the cost (in dollars) for a company to produce $ x $ pairs of a new line of jeans is $ C(x) = 2000 + 3x + 0.01x^2 + 0.0002x^3 $ (a) Find the marginal cost function. (b) Find $ C'(100) $ and explain its meaning. What does it predict? (c) Compare $ C'(100) $ with the cost of manufacturing the 101st pair of jeans.
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Step 1
Step 1: To find the marginal cost function, we need to find the derivative of the cost function $C(x)$ with respect to $x$. Show more…
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Suppose that the cost (in dollars) for a company to produce $x$ pairs of a new line of jeans is $$C(x)=2000+3 x+0.01 x^{2}+0.0002 x^{3}$$ \begin{equation} \begin{array}{l}{\text { (a) Find the marginal cost function. }} \\ {\text { (b) Find } C^{\prime}(100) \text { and explain its meaning. What does it }} \\ {\text { predict? }} \\ {\text { (c) Compare } C^{\prime}(100) \text { with the cost of manufacturing the }} \\ {101 \text { st pair of jeans. }}\end{array} \end{equation}
Derivatives
Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below. C(x) = 4000 + 5x + 0.01x^2 + 0.0002x^3 (a) Find the marginal cost function. C'(x) = (b) Find C'(60). (c) Find the actual cost of manufacturing the 61st pair of jeans. (Round your answer to two decimal places.)
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