You have a rectangular piece of cardboard that you want to fold into a box. It occurs to you that you can cut out an equal square from each corner of the rectangle, make a crease along each side and fold them up.
Suppose that the paper is 45 cm wide and 60 cm long. Now here's the question: how much should you cut from the corners to form the box with maximum capacity, and what would be the width, length and volume of the resulting box?