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    Question about Maximum and minimum volumes of a rectangular box

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    Find the maximum and minimum volumes of a rectangular box whose surface area equals 8000 square cm and whose edge length (sum of lengths of all edges) is 480 cm.

    See attached file for full problem description.

    © BrainMass Inc. brainmass.com October 9, 2019, 6:53 pm ad1c9bdddf
    https://brainmass.com/math/optimization/question-maximum-minimum-volumes-rectangular-box-101303

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    Solution
    f(x, y, z) = xyz, volume
    g(x, y, z) = 2xy + 2yz + 2xz - 8000
    h(x, y, z) = 4x + 4 y + 4 z - 480

    We have ...

    Solution Summary

    This solution finds the maximum and minimum volumes of a box with a given surface area and edge length.

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