My question is about having an LP in the standard form $Ax \leq b$ and the set of basic feasible solutions. For each basic feasible solution (bfs) does there exist an appropriate objective function $cx,$ such that this bfs is the optimal solution for this particular objective function?
My answer is yes, because the objective function is just a vector; therefore, for each bfs we can adjust the vector appropriately.
What's your opinion?