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The popcorn box problem |
2013-11-07 |
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From Dave:
We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4-corners of a sheet of card and then folding up.
What I want is to find the sizes of card that lead to integer solutions for the size of the cut-out, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3.
I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1.
Answered by Walter Whiteley. |
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