Maximize
$$z = 3x_1 + 2x_2$$
such that
\begin{align}x_1 – x_2 &\geqslant 1\\
x_1 + x_3 &\geqslant 3 \\
x_1, x_2, x_3 &\geqslant 0 \end{align}
One solution i see says common region is unbounded while in other source gives $Z_{\mathrm{max}}$ as $13$ at $(3,2,0)$.
Best Answer
The LP is unbounded, here are a couple of perspectives of the feasible region graphically:
We can observe that for any $x_1$ we choose, there will always be a bigger value of $x_1 + \lambda$ that will create a better $z$ such that $3x_1+2x_2 < 3(x_1 + \lambda) +2x_2$, as there's nothing in the model bounding $x_1$. Graphically, note that the objective function is a plane (in green) that traverses the feasible region like so:
which confirms this conclusion that it is forever increasing as it traverses $x_1$.