In my optimization class, we are now covering the basics which are just simple word problems to find absolute minima and maxima using calculus, but the wording of this problem has me completely confused:
We have a piece of cardboard that is $50$ cm by $20$ cm and we are going to cut out the corners and fold up the sides to form a box. We are asked to determine the height of the box that will give a maximum volume.
Despite my best efforts, I cannot figure out how the box is to be constructed from the piece of paper (cutting the corners). Can someone please show me how to get the function I am supposed to maximize and how to get there? I thank all helpers.