

Good luck! If anything, yesterday’s problem is motivating (if not challenging) because I’m trying to use it to learn the simplex algorithm (off mediocre online tutorials—doubly so considering I think the problem needs dual simplex [pun intended]). I’ve spent far more time with pencil and paper trying to understand the algorithm than actually try writing code for it.

Nice job! I initially thought about using reduced-row echelon form, but the matrices all had infinitely many real solutions so I couldn’t figure out how to proceed. Instead, I scanned Wikipedia for a bit, found the two-phase simplex algorithm, spent two days getting it to work on paper and another day implementing it.
And the reward?
I’m not even done because ~10% of the systems have non-integer optima, so I still need to use cutting planes to add extra constraints to get the integer optima.