I was wondering if someone could explain why Mathematica is stating the optimal vector is {1,0} instead of {0,0.5} in the following invocation of LinearOptimization:
LinearOptimization[
x + y, {x + y >= 1/2, x >= 0, y >= 0}, {x \[Element] Integers, y}]
{x -> 1, y -> 0.}
Cheers,
Dan
Wow, that’s a real humdinger! First I verified that LinearOptimization is indeed minimizing the objective (it correctly flags it as unbounded if I change the sign of the objective). I then tried changing the “1/2” to “0.5”, then 0.01, still getting the same answer as you did. Then I tried “1.01”, and got
{x->2, y->0.}
(This with Mathematica 12.3 on Windows 10).
Seems like a bug!
Same answer on 13.0.1 (Windows 10).