Question

Maximise $Z=x+y$, subject to $x-y\le -1,x-y\ge 0,x,y\ge 0$

Answer 1

The region determined by the constraints $Z=x+y$, subject to $x-y\le -1,x-y\ge 0,x,y\ge 0$ is as shown.
There is no feasible region and thus, $Z$ has no maximum value.