The Problem:
See reference diagram above.
Given a square of sheet metal with a side of length x, the task is to cut squares of side y from each of the 4 corners, then the edges folded to make a rectangular box open at the top. (See diagram) Then what value of y (in terms of x) will maximize the volume of the box. What is the maximum volume obtained?
Hint: Some algebra and differentia calculus will be needed for solution.
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