Consider a minimum cost network flow problem with lower bounds of 0 and upper bounds of on each arc, and m nodes. Suppose you are given an optimal solution with exactly m-1 arcs with positive flow. Provide a counterexample to show that this solution, along with a root arc with 0 flow, is not always a basic feasible solution. Consider a minimum cost network flow problem with lower bounds of 0 and upper bounds of on each arc, and m nodes. Suppose you are given an optimal solution with exactly m-1 arcs with positive flow. Provide a counterexample to show that this solution, along with a root arc with 0 flow, is not always a basic feasible solution. Consider a minimum cost network flow problem with lower bounds of 0 and upper bounds of on each arc, and m nodes. Suppose you are given an optimal solution with exactly m-1 arcs with positive flow. Provide a counterexample to show that this solution, along with a root arc with 0 flow, is not always a basic feasible solution.