9. (a). [10 points] Use the Maximum Flow Algorithm (and TORA, if you wish) to find the maximum flow from node O to node T in the directed network below with 7 nodes and 12 arcs. The number on each arc indicates the flow capacity on that arc. List each breakthrough path you find and the amount of flow sent along it, as well as the total maximum flow. (b). [4 points] Identity a set of arcs that comprise a minimum capacity cut. (c). [10 points] Now suppose that the number on each arc (i,j) in the network above indicates the distance from node i to node j. Use Dijkstra's Algorithm (and TORA, if you wish) to find a shortest path from node O to node T. Write out the arcs that comprise this shortest path from node O to node T, as well as the length of the path. (d). [10 points] Formulate the shortest path problem in part (c) as a binary integer programming programming problem. Write out the objective function and constraints that would be used to solve it as such. No need to solve it, however... you hopefully already did that using Dijkstra's Algorithm in part (c)