If we have

Y number of categories of building blocks.

Each category has X number of variants.

Each variant is associated with a unique cost.

One variant from each category is put together into an assembly.

Z number of assemblies are put together, arbitrarily using variants from each category.

Hypothesis: If total cost of each category is minimized, with respect to the number of each variant used in all assemblies – then total cost of all assemblies is also minimized. Is this true? Can it be proven mathematically? How?

Example:

Categories of building blocks: Tetraeders Cubes Oktaeders Spheres

4 Variants in each category: Red Blue Green Yellow

Total of 16 parts, we have one red, one blue one green and one yellow tetraeder etc....

Combine these together arbitrarily in 100 different assemblies with 4 parts each (one from each category).

Cost of each variant is randomly distributed between 1 and 100.