Almost! As I said earlier, it’s possible that the optimal value is infinite because of asymptotic directions. It’s also possible that there exists no feasible vector, which means that the feasible set is empty and no vector can be considered as an optimum. Aside from these two cases, a theorem says that there always exists an extreme point that is one of the points that maximize the objective function. It’s possible that other points also maximize the objective function. Still, it means that if we know all the extreme points of our feasible set, we can easily solve our problem by testing them all! That’s a great structure, isn’t it?