The Dumbells Soup Company makes its own cylindrical tin cans. The cans have a diameter of 3 inches and they are 3.5 inches tall.

Dumbells produces the cans by cutting out circles and rectangles from a large sheet of tin. The "wasted tin" between circles and rectangles that they cut out is thrown away. The company can order sheets of arbitrary length, but they are always 6 feet wide.

The operations manager just received an order for 100 cans. He should order the shortest length sheet of tin he can, because he is tasked with minimizing the wasted tin.

What length should the manager order?

(In reply to What are we buying again? by Jer)

The problem statement says they cut out "circles and rectangles". My natural assumption at first was they would cut 200 circles of diameter 3" for the tops and bottoms, and 100 rectangles of dimensions 3.5" x 3*pi" for the height of the cylinder. However, given that the problem never specifies that to be the case, I wonder if it were not possible just to cut out all the necessary circles, then cut out infinitely small rectangles from the "wasted tin"  and piece them together to get the appropriate sized rectangles, thereby wasting no tin.

Posted by Avin on 2004-11-12 14:50:23