It is clear to see that if the feasible region of a linear programming problem is nonempty and bounded, then the objective function attains both a maximum and minimum value and these occur at extreme points of the feasible region.
What if the feasible region of a linear programming problem is nonempty (do not know about boundedness) and the objective function is bounded in the feasible set? Can we conclude that the linear program has a finite optimal solution?
This intuitively seems true, but how do I go about proving it?