Consider the following 5 least-cost network flow problems on the same graph G = (N, A) which is shown below:

The following table shows the costs of each arch and the offers and demands of each node:

For each of the 5 problems, indicate whether it admits an optimal solution or not. Justify your answer.

1 1 3 2 4. Problema C13 C14 C21 C24 C32 C43 bi b2 b3 b4 - 1 2 1 - - 1 - 1 A B C D E 2 5 2 1 1 2 1 1 3 1 1 1 1 0 3 3 2 1 2 3 1 2 - 2 0 0 - 1 3 1 1 - 2 1 0 2 - 1 0 - 1 1 1 0 - 2 0 1 1 0 3 1 1 3 2 4. Problema C13 C14 C21 C24 C32 C43 bi b2 b3 b4 - 1 2 1 - - 1 - 1 A B C D E 2 5 2 1 1 2 1 1 3 1 1 1 1 0 3 3 2 1 2 3 1 2 - 2 0 0 - 1 3 1 1 - 2 1 0 2 - 1 0 - 1 1 1 0 - 2 0 1 1 0 3