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Math Help - Optimization Problem !

  1. #1
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    Exclamation Optimization Problem !

    Suppose the revenue (in thousands) for sales of x hundred units of an electronic item is given by the function R(x) = 40x^2e^-0.4x + 30, where the max capacity of the plant is eight hundred. Determine number of units for max revenue.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by madman1611 View Post
    Suppose the revenue (in thousands) for sales of x hundred units of an electronic item is given by the function R(x) = 40x^2e^-0.4x + 30, where the max capacity of the plant is eight hundred. Determine number of units for max revenue.
    R^{\prime}(x) = 80xe^{-0.4x} - 16x^2e^{-0.4x} = 0 <-- Solve for x

    80xe^{-0.4x} = 16x^2e^{-0.4x}

    5 = x

    (I leave it to you to prove that x = 5 is a local maximum, not a local minimum.)

    -Dan

    Edit: This problem would actually belong to a Calculus forum...
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    So you are saying the maximum number of units is 5, but the answer is 500 at back of book? Or am I totally confused. Thanks.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by madman1611 View Post
    Suppose the revenue (in thousands) for sales of x hundred units of an electronic item is given by the function R(x) = 40x^2e^-0.4x + 30, where the max capacity of the plant is eight hundred. Determine number of units for max revenue.
    Quote Originally Posted by madman1611 View Post
    So you are saying the maximum number of units is 5, but the answer is 500 at back of book? Or am I totally confused. Thanks.
    If you look at your original problem x is in units of 100.

    -Dan
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  5. #5
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    LOL. Dude, I've had that answer for a while ! Thanks bro. Think I should fully read the question first.
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