The​ cost, in​ dollars, of producing x belts is given by Upper C (x )equals 970 plus 12 x minus 0.076 x squared. The​ revenue, in​ dollars,

Question

The​ cost, in​ dollars, of producing x belts is given by Upper C (x )equals 970 plus 12 x minus 0.076 x squared. The​ revenue, in​ dollars, of producing and selling x belts is given by Upper R (x )equals 43 x Superscript three fourths . Find the rate at which average profit is changing when 484 belts have been produced and sold.

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Maya 2 weeks 2022-01-03T14:04:30+00:00 1 Answer 0 views 0

Answers ( )

  1. Charlotte
    0
    2022-01-03T14:05:41+00:00

    Answer:

    $68.44 for each additional belt

    Step-by-step explanation:

    The cost and revenue functions are:

    C(x) = 970+12x - 0.076x^2\\R(x) =43x^{\frac{3}{4}}

    The profit function, P(x), is given by subtracting the cost function from the revenue function.

    P(x) = R(x) - C(x)\\P(x)=43x^{\frac{3}{4}}+0.076x^2-12x-970\\

    The derivate of the profit function gives us the rate at which profit changes:

    \frac{dP(x)}{dx} =P'(x)=32.25x^{\frac{-1}{4}}+0.152x-12\\

    For x = 484, the rate of change is:

    P'(484)=32.25*484^{\frac{-1}{4}}+0.152*484-12\\P'(484) = \$68.44/belt

    Profit is increasing by $68.44 for each additional belt

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45:7+7-4:2-5:5*4+35:2 =? ( )