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25 September, 01:22

The equation for the cost in dollars of producing automobile tires is c = 0.000015x2 - 0.03x + 35, where x is the number of tires produced. find the number of tires that minimizes this cost. what is the cost for that number of tires?

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  1. 25 September, 03:41
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    The cost function is

    c = 0.000015x² - 0.03x + 35

    where x = number of tires.

    To find the value of x that minimizes cost, the derivative of c with respect to x should be zero. Therefore

    0.000015*2x - 0.03 = 0

    0.00003x = 0.03

    x = 1000

    Note:

    The second derivative of c with respect to x is positive ( = 0.00003), so the value for x will yield the minimum value.

    The minimum cost is

    Cmin = 0.000015*1000² - 0.03*1000 + 35

    = 20

    Answer:

    Number of tires = 1000

    Minimum cost = 20
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