1980s aluminum beverage can design optimization using supercomputers

Calculus-of-variations problem becomes industrially significant when volume is high and metal cost is twice steel.

Now let's talk about materials competition. The example I like to give is beverage containers. [Tom produces several cans.] We make some cans out of steel. We make some cans out of aluminum. This is an all-aluminum can. It actually has a different alloy at the top and on the sides, because you have to form this one by drawing and stretching. In this one you need some strength, and you've got to have the pull-tab that works. And of course there's plastics. There's glass — I could have brought in a piece of glass from my office. Each one has its own advantages and disadvantages.