Consider the following directed network. 6. 4 1 5 4 3 7 3 9 3 6 4 4 (a) (14 pts.) Assume that the numbers on the arcs in the network above are distances and use Dijkstra's algorithm to find the shortest path from node 1 to node 7. (b) (15 pts.) (i) An oil company operates the pipeline network shown above. Assume that each pipeline is labeled with its maximum flow rate in million cubic feet per day. The company has constructed a new oil well at node 1 and they would like to transport oil from this well at node 1 to their refinery at node 7. Formulate and solve a network optimization model to determine the maximum flow rate from node 1 to node 7. Also, find the optimal flow through each arc. (3 pts) (ii) Find a cut (e.g. a set of arcs) with total capacity equal to the maximum flow.