With Mathematica 7:
LinearProgramming[{1, 1}, {{0, 0}, {1, 1}}, {1, 1}, Automatic, Integers]
gives wrong result {0,1}
. But
LinearProgramming[{1, 1}, {{0, 0}, {1, 1}}, {1, 1}, Automatic, Reals]
gives correct error:
LinearProgramming::lpsnf: No solution can be found that satisfies the constraints.
From my point of view this is a buggy behaviour, or did I miss something? Can someone confirm this for newer Mathematica versions?