$$\max[Z(x,y)=3x+2y]$$
$$-x+y\le 1$$
$$-x+2y\le4$$
When I tried to solve the above maximization LP problem using the simplex method, from the first iteration, all basic variables became negative.
When I searched for an online tool to solve this LP problem, I found that no optimal solution exists.
How can I know that my LP problem has no optimal solution so that I can stop iterations?
Thanks in advance .
For any $x \geq 0$, set $y=\frac{x}{2}$, so that $-x + y = -\frac{x}{2} \leq 0 \leq 1$ and $-x + 2y = 0 \leq 4$. The constraints are satisfied, and the objective value is $$3x + 2y = 4x \xrightarrow[x\to\infty]{} +\infty$$ i.e. the objective is unbounded.