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Wonder Woman wants a box for her lasso. It is to be built from a rectangular piece of steel measuring 25 cm by 40 cm by cutting out a square from each corner and then bending up the sides. Find the size of the corner square which will produce a container that will hold the most.

Per suggestion by user Mark S, rewrote question to accept answer.

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I got the same answer, so probably yes. –  Angela Richardson Nov 7 '12 at 14:44
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Yes, this is correct. –  Brian M. Scott Nov 7 '12 at 16:18
    
@AngelaRichardson Do you study statistics, because you said probably yes? –  yiyi Nov 7 '12 at 22:57
    
@MaoYiyi, consider rewriting your proposed solution as an answer and accepting it. I came across this when viewing problems with no answers. –  Mark S. Jan 11 '13 at 17:26
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@MarkS. I have done that. –  yiyi May 30 '13 at 2:55
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2 Answers 2

up vote 1 down vote accepted

Now the volume of a box is Length * Width * Height

I am thinking that the length of the box is $(40{\ \rm cm} - 2x)$, where $x$ is the side of one of the corner squares cut out of the piece of steel. The width $= (25{\ \rm cm} - 2x)$ and the height $= x$.

This gives an expression $4x^3 - 130x^2 + 1000x$ for the volume, which has a max at $5$, thus the side of the squares cut out should be $5{\ \rm cm} \times 5{\ \rm cm}$.

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I am making this an answer rather than a comment, because I find the question itself upsetting.

There is enough misogyny in the world and on the internet that I object to the phrasing of this question in terms of "Wonder Woman's box" objectionable.

There are many different ways this exact same problem could be phrased, and, in my opinion, this is one of the worst.

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