How can I find the highest extreme point in an unbounded linear program / open polyhedron?

Question

Given the following open example polyhedron:

(1)  x1        >= 1  
(2)  x1 -x2 -s <= 0  
(3)  x1 +x2    <= 3  
(4)  x1        >= 0  
(5)      x2    &g