Explanation Lat h denote the height of the carton and s denote the side length of the square base. Clearly the volume will be maximized when the sum of the height and girth equal 108 4 s + h = 108 h = 108 − 4 s Allowing for degenerate cartons the volume V ( s ) = s 2 h = s 2 ( 108 − 4 s ) 0 ≤ s ≤ 27 Solve V ' ( s ) = 216 s − 12 s 3 = 0 Obtain s = 0 or s = 18 since V ( 0 ) = V ( 27

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4.6, Problem 30E

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According to postal regulation a carton classified “oversized” if the sun of its height and girth exceeds 108 find the dimension of a carton with a square base that is not oversized and has maximum volume

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Chapter 4.6, Problem 29E

Chapter 4.6, Problem 31E

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According to postal regulation a carton classified “oversized” if the sun of its height and girth exceeds 108 find the dimension of a carton with a square base that is not oversized and has maximum volume

Solution Summary: The author explains that a carton classified as "oversized" has maximum volume when the sum of its height and girth equals 108.

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According to postal regulation a carton classified “oversized” if the sun of its height and girth exceeds 108 find the dimension of a carton with a square base that is not oversized and has maximum volume

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