Section 6 Problem 2 - Beautiful - Shipping Balls in a Box - Minimize the Surface Area (that's material)

Reduce it to 2D - it's circles inside a rectangle - now minimize the perimeter. A lovely problem. When you ship the balls, you pay for material - who cares about the volume - you want to minimize the area of the material only. In the 3D case, the height is set by the largest. What about the W and L? That nicely, naturally, reduces to the 2D case..

Intuitively, it's about maximizing area while minimizing perimeter.

If the balls (there are three) aren't all touching each other and the edges, you're wasting space.

I guess you could just set this up with variables (positions of the three circles) and parameters (circle sizes) and let the optimizer handle it. You just need constraints that keep any two circles' centers r1 + r2 apart. (They can touch, but not overlap)

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