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Thread: Need help with setting up optimization problem

  1. #1
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    Need help with setting up optimization problem

    So, i got the following problem:

    A closed box with rectangular sides is built according to the following specifications: The top and bottom sides are made of a material that costs 5 dollars per square foot. the four vertical sides are made of a material that costs 3 dollars per square foot. The top and bottom sides are rectangles with sides of length x and y, where 2x = 7y. The total cost of materials is 100 dollars. Find the largest possible volume that such a box can hold.


    My functions are:

    Cost= 10xy + 12zy = 100
    V = xyz

    2x = y7

    I'm trying to put Volume in terms of one variable, but i cant... am i missing something?
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  2. #2
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    Re: Need help with setting up optimization problem

    take the cost function with

    $x = \dfrac 7 2 y$

    $35 y^2 + 12 z y =100$

    $z = \dfrac{100-35y^2}{12y}$

    now you have

    $V = x y z = \dfrac 7 2 y \cdot y \cdot \dfrac{100-35y^2}{12y} = \dfrac{7y(100-35y^2)}{24}$

    and this can be maximized in the usual way.
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  3. #3
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    Re: Need help with setting up optimization problem

    Omg thank. Didn't think that way!! Thanks
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