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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+132)

How many units?

  • math - ,

    C(x) is the total cost for x units, so the average cost is C(x)/x per unit.

    A(x) = C(x)/x = 0.2(0.01x + 132/x)
    to minimize A(x), find where dA/dx = 0
    dA/dx = 0.2(0.01 - 132/x^2)
    dA/dx = 0 when x = 20√33 = 114.89 = 115

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