Maximum product

Given a set A (greater than 3 elements) of digits (e.g. A = {1, 1, 2, 4, 4, 5, 5, 5, 7, 7, 8, 9, 9, 0, 0, 0, ...}), find the 2 numbers composed by ALL and ONLY the given digits, that produce the maximum (or minimum) product.

I could demonstrate a deterministic method for 4 digits.
For more digits I only found a technique that presumably works, but I couldn't demonstrate it. The algebra gets more complex.

Am I missing something?
Can anyone find a fast demonstration?

Regards,
Marco