Objective function $Z=x+y$, constraints
$$
x-y \leq-1,-x+y \leq 0 x, y \geq 0
$$


(i) The line $\mathrm{x}-\mathrm{y}=-1$ passes through $(-1,0)$ and $(0,1)$ putting $x=0, y=0$ in $x-y \leq-1$ we get $0 \leq-1$ which is not true.
$\Rightarrow \mathrm{x}-\mathrm{y} \leq-1$ lies on and above $\mathrm{AB}, \mathrm{x}-\mathrm{y}=-1$
(ii) The line $-x+y=0$ passes through $\mathrm{O}(0,0)$ and $\mathrm{C}(1,1)$ putting $x=0, y=1$ in $-x+y \leq 0$ we get $1 \leq 0$ which is not true.
$\Rightarrow-x+y \leq 0$ lies on and below OC.
(iii) $\mathrm{x} \geq 0$ lies on and on the right of $\mathrm{y}$-axis.
(iv) $\mathrm{y} \geq 0$ lies on and above $\mathrm{x}$-axis. There is no common region i.e., there is no feasible region.
There is no maximum value of $Z$.