a square of uniform size is cut from each corner of a piece of cardboard that is 20 by 30. Your job is to make a box with the largest possible volume.

Question

What should the length of the square be (rounded to two decimal places) to give you the maximum volume?

Answer 1

If  you cut a square with each side of length "x" from all 4 corners of a box, then fold what is left of each edge up, you will get a box with a height of "x".

 

So the long side is now 30-2x.  The short side is now 20-2x

 

The volume of the box is lwh = (30-2x)(20-2x)(x)

 

Multiply these out and graph it and find the x-coordinate of the tallest peak.

 

My calculator says the max is at x=3.92375 = 739/800 units