A manufacturer produces T-shirts for children. For this, thousands identical copies of the T-shirt form to the right have to be cut from a huge area of fabric. Since the T-shirt is composed as an addition or subtraction of rectangles and circles, it is fairly easy to compute its area (the lengths in the picture are in decimeter). The next picture shows how the T-shirts are drawn and cut from this large piece of material. Compute how many percent is waste. Find a more effective way of cutting these shapes from the material, producing less waste.
b) A more realistic model, however, considers also the expense of having to adjust the cutting machine. Few long cuts are less expensive than many short ones. Assume that to cut the neck half circle costs 10 cent, and cutting a straight line of length x (decimeter) costs 2x+5 cents. For which square meter price of the T-shirt cloth is your second method still cheaper than the one shown?
Erich Prisner, August 2003