How would you program this?

[Paul Rubin]

"Carl Banks" <invalidemail at aerojockey.com> writes:
> No kidding--it's a constrained integer programming problem.  Those can
> be pretty nasty.  This one is pretty simple, being linear with only 12
> unknowns.  However, they get very difficult very fast.  There are whole
> optimization textbooks written on this kind of problem.

Why is it an integer programming problem rather than just a set of
simultaneous equations?  It looks offhand like 12 equations in 12
unknowns that can be solved with linear algebra, but I haven't tried
solving it.