# Tin Box with Maximum Volume

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Problem: A piece of sheet tin three feet square is to be made into a rectangular box open at the top by cutting out equal squares from the corners and bending up the sides of the resulting piece parallel with the edges. Among all such boxes, to find the box of greatest volume.

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Contributed by: Roger B. Kirchner (July 2009)

Open content licensed under CC BY-NC-SA

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Former Harvard Professor Joseph Leonard Walsh expanded on his 1947 Classroom Note in a 1962 booklet [2] concerned with rigor in finding global maximum and minimum values. He argued the second derivative is unnecessary.

[1] J. L. Walsh, "A Rigorous Treatment of the First Maximum Problem in the Calculus," *The American Mathematical Monthly*, 54(1), 1947 pp. 35–36.

[2] J. L. Walsh, *A Rigorous Treatment of Maximum-Minimum Problems in the Calculus*, Boston: Heath, 1962.

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