Assume we are given a linear programming problem. It is well-known that a linear programming problem is unbounded iff there exists an EXTREME direction $d$ such that cd>0 (consider maximization case). Now, I want to check whether my LP is unbounded. I described the existence of a recession direction in the feasible area of the given linear programming problem using constraints 2,3 and constraint (1) is for unboundedness.
2) $Ad \leq 0$;
3) $Bd \leq 0$;
After checking the feasibility of the above polyhedral, I have two directions. First, the polyhedral is infeasible. In this case for sure the problem is bounded (Since I could not find any feasible and also basic feasible solution for the corresponding LP). Second, what if the polyhedral is feasible? Then, can I say that I have an EXTREME ray $d$ with $cd>0$ ?