The first thing “e” wanted to do is to “Calculuize” his favourite game, apples to apples. So, one day, his friend, pi worked with “e” to do the following experiment. They decided to construct a box for the apples to apples game such that its width is exactly three times its length and its volume is 36 cubic centimeters. Assuming that the box is closed on all sides and using calculus methods only, determine the smallest amount of material needed for its construction. Show all your work.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 75E
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The first thing “e” wanted to do is to “Calculuize” his favourite game, apples to apples. So, one day, his
friend, pi worked with “e” to do the following experiment.


They decided to construct a box for the apples to apples game such that its width is
exactly three times its length and its volume is 36 cubic centimeters.


Assuming that the box is closed on all sides and using calculus methods only,
determine the smallest amount of material needed for its construction. Show all
your work.

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