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10 April, 01:50

g:dollars to manufacture x units of a device in an hour at one of their manufacturing centers. How many devices should be manufactured each hour to minimize average cost?.002x+160 units What is the resulting average cost of a device? $ How does the average cost compare with the marginal cost at the optimal production level? Find how much they differ.

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  1. 10 April, 01:56
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    - How many devices should be manufactured each hour to minimize average cost? * *21000* * units.

    - What is the resulting average cost of a device? $ 441160.001

    - How does the average cost compare with the marginal cost at the optimal production level? Find how much they differ. $ 0.00

    The marginal cost and the average cost are absolutely the same at the optimal cost.

    Explanation:

    C (x) = 441000 + 160x + 0.001x²

    Average cost = (Total cost) / (number of units)

    Average cost = (441000/x) + 160 + 0.001x

    At minimum average cost,

    dAC/dx = 0 (Note: AC means average cost)

    dAC/dx = - 441000/x² + 0.001

    when it is equal to 0

    - 441000/x² = - 0.001

    x² = 441000/0.01 = 441000000

    x = 21000 units

    Average cost of a device.

    Average cost = (441000/x) + 160 + 0.001x

    For one device, x = 1

    average cost = (441000/1) + 160 + 0.001 (1)

    Average cost of a device = 441000 + 160 + 0.001 = $ 441160.001

    At optimal level, that is, x = 21000 units

    Average cost = (441000/x) + 160 + 0.001x = (441000/21000) + 160 + 0.001 (21000) = $202

    Marginal cost = dC/dx (Rate of change of total cost with the number of units)

    C (x) = 441000 + 160x + 0.001x²

    Marginal cost = (dC/dx) = 160 + 0.002x

    At x = 21000 units

    Marginal cost = 160 + 0.002 (21000) = $202

    The marginal cost and the average cost are absolutely the same at the optimal cost.
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