Problem #3 Consider the following directed network structure shown in Figure 2 representing a series of cities connected by highways. Formulate and solve a Linear Programming Model to find the shortest path for a passenger bus whose Origin (O) is City 1 and Destination (D) is City 7. Assume the numbers on the arcs are distances in miles. 10 2 5 6 3 4 1 4 7 7 8 4 4 9 3 6 Figure 2: Network Structure 1. Write the complete linear programming formulation as a series of mathematical linear equations containing decision variable's, objective function, and constraints. 2. Using Solver Functionality on MS Excel in order to clearly identify the shortest path between City 1 and City 7. 3. Does the model have multiple optimal shortest paths? How did you confirm whether the model has multiple optimal paths or not? 4. Discuss one additional potential industrial application of the shortest path LP model