Posted by kaa on Friday, January 17, 2014 at 11:16am.
You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. The cardboard measures 10 in. by 12 in. What are the dimensions of the box that will have greatest volume if the possible corner cuts measure 1 in., 2 in., 3 in., or 4 in.?

Calc  Steve, Friday, January 17, 2014 at 11:25am
well, the volume is width * length * height (x)
v = (102x)(122x)(x)
now plug in x=1,2,3,4 and see which gives the greatest volume

Calc  kaa, Friday, January 17, 2014 at 11:33am
a.9 in. by 12 in. by 1 in.
b.3 in. by 6 in. by 4 in.
c.7 in. by 10 in. by 2 in.
d.5 in. by 8 in. by 3 in.
c?

Calc  Steve, Friday, January 17, 2014 at 11:52am
Nope. Think about it. Since the two original dimensions are 8x10, after the cuts, the base of the box will be
8x10
6x8
4x6
2x4
You cannot even get (c) by cutting equal squares from all corners.
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