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17 November, 14:03

Suppose the total cost function for manufacturing a certain product C (x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)

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  1. 17 November, 14:20
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    C (x) = 53 $

    Step-by-step explanation: Incomplete question. From google the question is (paste)

    Suppose the total cost function for manufacturing a certain product C (x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)

    C (x) = 0.2 (0.01x^2+133)

    If C (x) = 0.2 (0.01x^2+133); and x numbers of produced units, the average cost is

    Ca (x) = (0,002*x² + 26,6) / x ⇒ Ca (x) = 0.002*x + 26.6/x

    Taking derivatives on both sides of the equation

    Ca' (x) = 0.002 - 26.6/x² Ca' (x) = 0

    0.002 - 26.6/x² = 0 ⇒ 0.002x² - 26.6 = 0

    x² = 26.6 / 0.002

    x = 115,33 ⇒ x = 115 units

    And the level of production will be

    C (x) = 0.2 (0.01x^2+133)

    C (x) = 0.002*x² + 26,6

    C (x) = 26.45 + 26,60

    C (x) = 53.05 $

    C (x) = 53 $
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