You want to create a box without a top from an 8.5 in by 11 in sheet of paper. You will make the box by cutting squares of equal size from the four corners of the sheet of paper. If you make the box with the maximum possible volume, what will be the length of the sides of the squares you cut out?
I'm not sure how to start this out. Do I multiply x(8.5-2x)(11-2x)?
3 answers
Well, assuming there is no bottom to the box (taken from where the instructions say you only cut 4 pieces of paper), the largest length possible that can be cut along the 8.5 in side is 4.25 inches. So, assuming the constraints from the instructions the way I interpreted, that is the length.
The volume V will be
V = (8.5 - 2x)(11 - 2x)x
V = 4x^3 - 39x^2 + 93.5x
Taking the first derivitive:
dV = 12x^2 - 78x + 93.5
Set equal to zero and solve for x.
V = (8.5 - 2x)(11 - 2x)x
V = 4x^3 - 39x^2 + 93.5x
Taking the first derivitive:
dV = 12x^2 - 78x + 93.5
Set equal to zero and solve for x.
What if the paper is 8.5 x 8.5?
1 answer