The real world version:
I have a united value (e.i. 12in, 120V 1.414 kg*m/s) where the units are specified as the rational exponents of the 5 base units; m, s, kg, C and K. Additionally, I have a set of non-base units and I want to find the "simplest" combination of those units that matches my value.
The abstract version:
With a little manipulation this can be converted to a very under defined linear combination problem. With a little more work it can be restricted to integer solutions, making it (I think) a linear programming problem (a subject I know almost nothing about).
The part I actualy care about:
What additional constraints/criteria can be applied to this problem to make it solvable and what are the implications of the options? Specifically, I'm looking for a solution that is well documented, simple to evaluate and produces approximately the same results as people would expect.