A linear program with unbounded optimal solution

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Consider the following

$$\max 3x_1+x_2\\ s.t. -x_1+2x_2\le0\\ x_2\le4$$

a) Sketch the feasible region

b)Verify that the problem has an unbounded optimal solution value

Attempt:

a) (Here the region looks bounded but it's unbounded, sorry I don't know how to use Mathematica very well..) enter image description here

b) I tried to use the simplex algorithm but when taking the pivot column which was $[-1\ 0\ -3]^T$ and trying to divide by the other column (the last one of the tableu) $[0\ 4\ 0]^T$ I got $\frac{0}{-1}$ ,4/0,$\frac{0}{-3}$, I got a division by $0$.

What can I do here?

How can I do b) with this?

Could someone help me please?