Humber Electrical Wire Packing Project

A Humber Electrical Engineering Technology student needs to pack electrical wire for shipping to Carrier campus. They have a stack of square cardboard pieces that need to be turned into open top boxes. The boxes will be made by cutting out equal sized smaller squares from the corners of each piece of cardboard and the sides then folded up. What size should the smaller squares be to optimize the volume of the box? The original piece of cardboard is a big square with 4 congruent smaller squares (each having side length x) that are each cut from the corners of the larger square. The 4 rectangular pieces that remain are then folded up to create a rectangular box with open top.