Problem 1 (15 points): Given the network below, solve the one to all shortest path problem as a network flow problem using GAMS. Provide a graphical depiction of the shortest path tree in your solution. Cij j 8 2 1 2 6 5 7 2 3 3 3 5 8 Problem 2 (5 points): Modify your code to find the shortest path from node 1 to node 6 only. Solve the problem using GAMS. Provide a graphical depiction of the shortest path in your solution. Problem 3 (10 points): If there is 1 unit of demand at node 6, 2 units of demand at node 7, and 2 units of demand at node 8, what is the optimal assignment of flow to the network? Solve as a min cost flow problem using GAMS. Capacities are given in the provided include file. Report optimal link flows and objective function value. Problem 1 (15 points): Given the network below, solve the one to all shortest path problem as a network flow problem using GAMS. Provide a graphical depiction of the shortest path tree in your solution. Cij j 8 2 1 2 6 5 7 2 3 3 3 5 8 Problem 2 (5 points): Modify your code to find the shortest path from node 1 to node 6 only. Solve the problem using GAMS. Provide a graphical depiction of the shortest path in your solution. Problem 3 (10 points): If there is 1 unit of demand at node 6, 2 units of demand at node 7, and 2 units of demand at node 8, what is the optimal assignment of flow to the network? Solve as a min cost flow problem using GAMS. Capacities are given in the provided include file. Report optimal link flows and objective function value