Interesting Optimization Problem Related to Information Gain

I've been thinking of the problem of how to supply information to a neural network. Given that I have a defined amount of information (e.g x + y + z + a = 100), how can I maximize the volume of the neural net. In a simple case, this optimization problem can be formed as:

(x¹⁾ x (y²⁾ x (z³⁾ x (a⁴⁾ where x+y+z+a=100.

The trick is, it's not to put them all evenly, or even put them so that the weight sights toward the a^4. It's been bothering me for about a week now, and I don't know any methods that solve this kind of optimization.

Here's a start to see why:

(25¹⁾ x (25²⁾ x (25³⁾ x (25⁴⁾ = 9.53x10^13, which is essentially 25^10. So we take 1 from the (25⁴⁾ and distribute to each and make it (28³⁾ x (24^7).. which if you break it down is just a simplification of (24¹⁾ x (24²⁾ x (28³⁾ x (24⁴⁾ = (24⁷⁾ x (28³⁾

and that makes (28³⁾ x (24⁷⁾> 25¹⁰

This problem may have many local maxima and many local minima, could I get some insight on this?

Thanks!