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29 July, 22:01

A manufacturer has fixed costs of $16,000 per month and can produce w widgets at a cost of 0.1w^ (2) + 20w. How many widgets should be produced monthly to minimize the cost per widget?

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  1. 29 July, 23:56
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    Consider c as the cost of the widget so that our given equation is

    c = 0.1w^2 + 20w

    Take the derivate of the equation.

    d/dt (c = 0.1w^2 + 20w)

    dc/dt = 0.2w + 20

    Given dc/dt = $16000 per month, the number of widgets would contain:

    16000 = 0.2w + 20

    -0.2w = 20 - 16000

    -0.2w = - 15980

    w = 79900 widgets
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