Warm-up:

I have four rods of length x and four rods of length y. How many ways can I combine these to make two rectangles, and which configuration produces the greatest total area?

The problem:

I have twelve rods of length x, twelve rods of length y, and twelve rods of length z. How many ways can I combine these to make three cuboids, and which configuration produces the greatest total volume?

(For example, I could simply make a cube of side length x, a cube of side length y, and a cube of side length z.)

Note - I think that proving you have the greatest volume is fairly difficult, so I would be happy to receive and mark partial solutions!