How could I go about the problem finding the extreme rays of a polyhedral defined by constraints
$x_1-x_2 \geq -2$
$x_1+x_2 \geq 1$
$x_1,x_2 \geq 0$
I know for certain that given a max or min problem in standard form, using the simplex method, if the optimal cost is at -∞, then the algorithm will terminate at an extreme ray. My issue here is that the problem just defines constraints with no objective function.