Please guide me on the following question.
Consider the LP problem
Which of the following is true?
$1.$ The LP problem admits an optimal solution.
$2.$ The LP problem is unbounded.
$3.$ The LP problem admits no feasible solution.
$4.$ The LP problem admits a unique feasible solution.
The first line passes through $(0,-5)$ and $(10,0)$. The second line passes through $(0,10)$ and $(-5,0)$. They both intersect at (-10,-10). Thereby, I am getting that it would be an unbounded problem and won't have any feasible solution.
That is, according to me, $2nd$ and $3rd$ options are correct. But answer should be only one option. Please help.