The following problem was given to me by a friend .
Find all vertices, extremal rays, and extremal lines of the following polyhedron. $$ P = \left\{ x ∈ \Bbb R^3 : 2x_1 − x_2 \ge 2, x_1 + x_2 \ge 1, −x_1 + x_2 \ge 2, x_i \ge 1, i = 1, \dots , 3 \right\} $$ Prove that you have really found all vertices, extremal rays and extremal lines.
I can't for the life of me figure out what to do. I am just completely lost and would be extremely grateful if someone could help so I can to these problems with no issue in the future.
I got $(1,0,0)$, $(0, 1, 0)$, $(0,2,0)$ and $(1,1,1)$. Is this correct?