Question

Hey I'm having a lot of trouble with this question.
An open box is to be made from a 20 inch by 40 inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. A) What size should the squares be in order to obtain a box with the largest volume? B) What are the dimensions of the box? C)What is the maximum volume of the box?
could you show me how to solve it step-by-step?

Answer 1

If the cut is x inches, then the length and width are reduced by 2x, and the height is x. So the volume is

v = x(40-2x)(20-2x) = 4x^3-120x^2+800x

I can't believe that finding the maximum value of such a function is a topic for pre-algebra! It requires either analysis of a graph, or numerical methods, or calculus.

You can see information about the function at

http://www.wolframalpha.com/input/?i=x(40-2x)(20-2x)