Problem #2. Consider the following network structure shown in Figure 1 representing a series of cities that must be visited by a truck driver working for a Logistics Company. The starting city of this Truck Driver is situated at Node 1 and his goal is to visit all the cities and then return back to Node 1. Given a list of cities and the distances between each pair of cities, develop a LP Model to find the shortest possible route that visits each city exactly once and returns to the origin city. Note: The distances between the cities are represented on the arcs connecting them. The arcs or line segments between the nodes are bi-directional. Meaning, the truck can travel in either direction between the two nodes. 2 15 13 13 9 16 Figure 1: Network Structure Please answer the following questions: 1. Write the complete linear programming formulation using the index notation discussed in class. 2. Write the complete linear programming formulation as a series of mathematical linear equations containing decision variable's, objective function, and constraints. 3. Determine an Optimal Tour for the truck driver. 4. Explain how you arrived at the Optimal Tour and write down all the subtour elimination constraints that you had to introduce to your initial LP model in order to arrive at the optimal tour. 5. Does this model have multiple optimal paths? Explain how you identified and generated the other optimal path if one does exist. 6. Discuss one additional potential industrial application of this model