ineq = {x >= 0, y >= 0, z >= 0, 2 x >= y, 2 z >= y, 2 x + y <= 4, 2 z + y <= 4}; And @@ (ineq /. Thread[{x, y, z} -> {2, 4, 0}]) And @@ (ineq /. Thread[{x, y, z} -> {0, 0, 0}])
