3. 20 Points Consider the following new ch vertices r and y are the source and sink respectively, and the number next to edge is its capacity. 13 10 9 38 りに 1 18 27 (a) Use the algorithm from class to find zero-flow. Explain your work and next to each edge indicate the flow along this edge (Write maximum flow in this network, Begin with the in red to distinguish it from the capacity) (b) What is the value of your Aow? (c) Prove that your flow is a maximum flow. In each figure For problem 3. You may wish to use the figures below to show your work. Mous. battleneck int n path and ind edge Write the curent now hext to each e e). Then in the next figure show the increased flow, an augmenting path for this flow, and so on.. G 13 13 10 18 31 27 C augmenting path augmenting path in red, tolerance: red, tolerance: 13 15 10 38 d 27 C C red, tolerance: augmenting path in red, tolerance augmenting path 13 13 10 10 38 38 8 1 1 augmenting path in red, tolerance: red, tolerance: augmenting path a e 13 13 1 10 10 38 38 G 27 27 augmenting path in red, tolerance: red, tolerance: augmenting path