SOLUTION: A box is to be made from a rectangular piece of cardboard by cutting a square from each corner and folding up the sides. The rectangular piece of cardboard is originally 10 inches

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Question 1038812: A box is to be made from a rectangular piece of cardboard by cutting a square from each corner and folding up the sides. The rectangular piece of cardboard is originally 10 inches long and 40 inches wide, and the squares removed from the corners are x inches wide. The volume of the box is given by the function V=x(10-2x)(40-2x). What restrictions must be placed on x to satisfy the conditions of this model? In other words, what is the domain of this function?
I know the answer is 0 < x < 5, but how do I find this? I did manage to get x=20 and x=5, however I don't understand how one is picked over the other.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Clearly, if then you have no box since the area cut out of the corners is zero. If you cut 5-inch squares out of the corners of a 10 by 40-inch piece of cardboard, then you would have a 10-inch by 30-inch piece of cardboard that you would fold in half lengthwise. Again, no box. Cutting a 20-inch square out of the corner of a 10 X 40 piece of material is impossible. You can go 20 inches along the 40-inch dimension, but you can't go 20 inches the other way. Anything between 0 and 5, NOT inclusive, makes a box, but there is only one value that gives you a maximum volume in that interval.

John

My calculator said it, I believe it, that settles it