objective:min $−3x_1−2x_2−x_3$
The set is : $X=\lbrace (x_1,x_2,x_3):2x_1+x_2-x_3\le2; x_1,x_2,x_3\ge0 \rbrace$
Attempt:
$2d_1+d_2-d_3\le0$ (a)
$d_1+d_2+d_3=1$
and $d_1,d_2,d_3\ge0$
Since from (a),we have $-d_3$, one extreme direction could be $ d^1=(0,0,1)$. Then half this, $d^2=(0,1/2,1/2)$, and similarly $d^3=(1/3,0,2/3)$.
Is there any systematic way finding them?