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27 August, 08:17

The cost, in millions of dollars, for a company to manufacture x thousand speed boats is given by the function C (x) = 3x2 - 30x + 175. Find the number of speedboats that must be produced to minimize the cost.

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  1. 27 August, 08:19
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    5000

    Step-by-step explanation:

    In vertex form, the cost function is ...

    C (x) = 3 (x² - 10x) + 175 = 3 (x² - 10x + 25) + 175 - 3 (25)

    C (x) = 3 (x - 5) ² + 100

    The vertex is at x=5, so the cost function will be minimized when 5000 speed boats are produced.
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