MAT103

Franklin College

Erich Prisner

### Writing Project 17:

# T-Shirt Production

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?