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