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27 January, 22:37

A company that manufactures mountain bikes makes a daily profit p according to the equation p equals negative 100 x squared plus 4900 x minus 57 comma 424 , where p is measured in dollars and x is the number of mountain bikes made per day. Find the number of mountain bikes that must be made each day to produce a zero profit for the company.

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  1. 27 January, 23:33
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    x is approximately 9 or 58.

    Step-by-step explanation:

    p = - 100x^{2} + 4900x - 57,424

    to find x, when p = 0

    0 = - 100x^{2} + 4900x - 57,424

    Using the almighty formular

    x = (-b ± √b^2 - 4ac) / 2a

    x = (-4900 ± √ (4900) ^2 - 4 (-100) (-57,424) / 2 (-100)

    x = (-4900 ± √24010000+22969600) / -200

    x = (-4900 ± √46979600) / -200

    x = (-4900 ± 6854.2) / -200

    x = (-4900 + 6854.2) / -200 or x = (-4900 - 6854.2) / -200

    x = - 9.7 or 58.7

    x is approximately 9 or 58.
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