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Math Help - volume optimization

  1. #1
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    volume optimization

    How do I go about doing this problem:

    A box with a square base and open top must have a volume of 32000 cm3. Find the dimensions of the box that minimize the amount of material used.
    1 cm (length and width)
    2 cm (height)

    Thanks!
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  2. #2
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    Quote Originally Posted by skeltonjoe View Post
    How do I go about doing this problem:

    A box with a square base and open top must have a volume of 32000 cm3. Find the dimensions of the box that minimize the amount of material used.
    1 cm (length and width)
    2 cm (height)

    Thanks!
    Let s = the side of the base

    Let h = the height of the box

    The area of the base is s^2

    The area of the 4 sides is 4sh

    You want to minimize M=s^2+4sh

    The volume must be 32000 so s^2h=32000

    h=\frac{32000}{s^2}

    M=s^2+\frac{128000}{s}

    Find the derivative of M, set it equal to 0 and solve for s. Then solve for h.
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