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Thread: Derivative: finding profit equation; maximizing profit

  1. #1
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    Derivative: finding profit equation; maximizing profit

    The question is:

    The revenue (in dollars) from the dale of "x" dinners is given by:

    . . .R(x) = -0.00000183x^3 - 0.00029532x^2 + 30.1898x

    and the cost (in dollars) of producing "x" dinners is given by the function:

    . . .C(x) = -0.001x^2 + 11x + 13000

    a) I need to find an equation for profit as a function of the number of dinners sold.

    b) I need to find the profit when 2300 dinners are sold.

    c) I need to use a derivative to find how many dinners need to be sold to maximize profit. What is the maximum profit?

    THANKS~

    K
    Kaye

  2. #2
    Senior Member skeeter's Avatar
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    Re: Derivative

    Quote Originally Posted by kjones
    The question is:

    The revenue (in dollars) from the dale of "x" dinners is given by:

    R (x) = -0.00000183x^3 - 0.00029532x^2 + 30.1898x

    and the cost (in dollars) of producing "x" dinners is given by the function:

    C (x) = -0.001x^2 + 11x + 13000




    a) I need to find an equation for profit as a function of the number of dinners sold.

    this is easy ... Profit = Revenue - Cost

    b) I need to find the profit when 2300 dinners are sold.

    evaluate your profit function found in part a) for x = 2300

    c) I need to use a derivative to find how many dinners need to be sold to maximize profit. What is the maximum profit?

    take the derivative of your profit function, set it equal to 0, and maximize

    K

  3. #3
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    Skeeter,

    can you help me with part c) the derivative?

    K
    Kaye

  4. #4
    Senior Member skeeter's Avatar
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    the profit function is just a basic polynomial ... show me its derivative and I'll help with the maximization.

  5. #5
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    In part a):

    I need to find an equation for profit as a function of the number of dinners sold.

    this is easy ... Profit = revenue - cost

    So, the
    Profit = -0.00000183x^3 - 0.00029532x^2 + 30.1898x ??


    K
    Kaye

  6. #6
    Senior Member skeeter's Avatar
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    no ... try again.

    P(x) = R(x) - C(x)

    P(x) = (-0.00000183x^3 - 0.00029532x^2 + 30.1898x) - (-0.001x^2 + 11x + 13000)

    P(x) = ?

  7. #7
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    P(x) = 301866638 - 13109.9 = -$12808.032

    K
    Kaye

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