The Open Box Problem

... Introduction The Open Box Problem A square piece of card has four equal sized squares cut out from each of it's four corners and is folded to make an open top box. The problem is to find out which value of x (the side length of the cut out) will maximise the volume in the resulting box, which is equivalent to the height (x) * the width (the side length of the square - 2x) * the depth (the same value as the width). This problem can be expanded to finding the maximised volume for a box that is made from a rectangular piece of card. Methods of Finding the Solution to the Problem - Trial and Error Approach There are two main ways of finding the solution to the problem. The first is a trial and error approach. For square pieces of card, a table is constructed showing the cut out side length

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