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I am looking for some insights on a standard calculus problem: "Find the maximum volume of a box formed by cutting squares from the corners of a rectangular piece of cardboard, then folding the resulting piece into a box". I know how to show the calculus involved in solving the problem. My question is, does anybody have any real-world insights to other factors, (manufacturing, marketing, ergonomics, etc.) that influence the size of, for instance, cereal boxes? I doubt they are the size they are solely due to maximum volume considerations. (I realize I am mixing 'closed top' and 'open top' boxes here, but you get the idea). Thanks in advance to any insights that will help me come up with an impressive presentation on this topic!
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