For a rectangular cardboard box of given dimensions, pack it as densely as possible with (say) 1 L bottles of a shape or shapes of your choosing, minimizing the amount of material constructing the bottles. Unlike the Kelvin cell or Weaire-Phelan cell, this is a finite packing, so there are edge effects.
Optimization problem to maximize profit: revenue per bottle, cost of material to create the bottle, set up cost per bottle mold -- the fewer the different shapes, say, around the edges, the better. Empty unused space might still be economical.
Inspired by, square bottles pack better than cylindrical.
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