For the linear programming problem:$\text{Maximize }Z=3X_1+2X_2$ Subject to:$-2X_1+3X_2\le 9$$X_1-5X_2\ge -20$$X_1,X_2\ge 0$ The above problem has:

To find the solution, we plot the constraints:$-2X_1+3X_2=9$: Passing through $(0,3)$ and $(-4.5,0)$. The region is towards the origin.$X_1-5X_2=-20\Rightarrow -X_1+5X_2=20$: Passing through $(0,4)$ and $(-20,0)$. The region is below/towards the line for the $\ge -20$ condition.When plotting in the first quadrant ($X_1,X_2\ge 0$), the feasible region is open-ended towards the right (as $X_1$ increases).Since the objective function $Z=3X_1+2X_2$ increases as $X_1$ and $X_2$ increase, and the region is not bounded in the direction of increasing $X_1$, the solution is unbounded.