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?

If these are tin cans we shouldn't order aluminum anyways, so the easy answer is: none.

'Tin' cans are made from galvagnized steel nowadays, aren't they.  Those dumbells.

A lower bound, strictly by area is (200*pi*1.5^2 + 100*3.5*3*pi)/72 = 58.905 inches

I doubt I could prove an optimal solution, but I'm willing to try.

-Jer

Posted by Jer on 2004-11-12 13:26:00