Problem 1. The network in the figure below gives the permissible routes and their lengths in miles between cities (nodes 1 to 8). In the four questions that follow, you will find the shortest route between two cities. For all cases, set-up the integer programming problem and numerically solve. 4 3 1 2 3 2 5 5 8 2 3/ 6 1 2 5 6 4 7 8 1. Determine the shortest route from city 4 to city 8 (node 4 to node 8). (Answer: There are two optimal solutions, resulting in a distance of 8 miles. They are routes 4-5- 6-8 and 4-6-8.) 2. Determine the shortest route from city 1 to city 8 (node 1 to node 8). 3. Determine the shortest route from city 1 to city 6 (node 1 to node 6). 4. Determine the shortest route from city 2 to city 6 (node 2 to node 6)