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 Tin Can Company (Posted on 2004-11-12)
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?

 No Solution Yet Submitted by SilverKnight Rating: 2.7500 (4 votes)

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 Calculus? | Comment 10 of 11 |
I haven't bothered to read all preceding postings, but a fair amount. Has anyone thoguht to use the basic optimization technique taught in highschool? That is, find a couple equations, assign a few variables, take the derivative, set it to zero, and then solve for "l" at all critical points? or taking the second derivative may suggest that the critical point is the absolute minimum, eliminating some of the work. Perhaps it cant be done, i havent sat down and tried, but it seems to me that it may yield a solution.

Now that ive thought about it: that may only tell you the least amount of material needed... it wouldnt account for waste between shapes.

Do what you can with my suggestion.

 Posted by Mike on 2005-01-12 16:41:26

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