Maximize $Z=2X_1+3X_2$ subject to $2X_1+X_2\le 6$, $X_1-X_2\ge 3$, $X_1,X_2\ge 0$. The solution to the LPP is:

Plotting the constraints:$2X_1+X_2=6$: Points $(3,0)$ and $(0,6)$. Region is towards the origin.$X_1-X_2=3$: Points $(3,0)$ and $(0,-3)$. Region is away from the origin (to the right).The only point that satisfies $2X_1+X_2\le 6$, $X_1-X_2\ge 3$, and $X_1,X_2\ge 0$ is the point $(3,0)$.Since there is a feasible point that gives a finite value for $Z$, the solution is optimal (specifically, a unique point solution).