# boundedness of a linear programming [closed]

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.

1) $cd>0$;

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 $cd>0$ ?

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 You shouldn't use this site for posing theoretical questions that have no computational aspect. – Arnold Neumaier Jul 18 '12 at 14:49 You may want to post this on the Math SE site. – Paul♦ Jul 19 '12 at 14:34

## closed as off topic by Arnold Neumaier, Aron AhmadiaJul 18 '12 at 18:52

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