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23 September, 17:34

The function C (x) = 600x - 0.3x2 represents total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold.

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  1. 23 September, 17:50
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    C (x) = 600x-0.3x²

    1) we calculate the first derivative

    C' (x) = 600-0.6x

    2) We math the firts derivative to 0; and we find out the value of "x"

    600-0.6x=0

    -0.6x=-600

    x=-600/-0.6

    x=1000

    3) we calculate the second derivative:

    C'' (x) = - 0.6; because - 0.6>0; we have a maximun at x=1000.

    4) We find out the maximum cost.

    C (1000) = 600 (1000) - 0.3 (1000) ²

    C (1000) = 600000-300000

    C (1000) = 300000

    Answer: the maximum cost is $300000
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