Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 20,000 + 15xex/700. Find the marginal cost when

Question

Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 20,000 + 15xex/700. Find the marginal cost when 700 units are produced. (Round your answer to the nearest cent.)

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Julia 1 week 2021-09-13T22:40:55+00:00 1 Answer 0

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    2021-09-13T22:42:45+00:00

    Answer:

    $ 1905.52

    Step-by-step explanation:

    C(x) = 20000+15xe^{x/700}

    The marginal cost is the derivative of C(x).

    By applying product rule of differentiation (and using the fact the derivative of a constant is 0, thereby ignoring 20000),

    \dfrac{d}{dx}C(x) = x\dfrac{d}{dx}e^{x/700} + e^{x/700}\dfrac{d}{dx}x

    M(x) = \dfrac{d}{dx}C(x) = \dfrac{x^2}{700}e^{x/700} + e^{x/700} = e^{x/700}\left(\dfrac{x^2}{700}+1\right)

    When x = 700,

    M(700) = e^{700/700}\left(\dfrac{700^2}{700}+1\right) = 701e = 1905.52

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