1. Formulate an integer program to find the shortest graph from node 1 to node 4 in Figure 1. Does Figure 1: A directed graph with four nodes (the number next to each arc is the arc length). the LP relaxation of your integer program have an integer optimal solution? Now consider a general directed graph G (N, A), where N is the set of nodes, A is the set of arcs, and cij is the length of arc (i,j) E A. Assume that c20 for each (i.j) A. Given two nodes s,te N, try to formulate an integer program to find the shortest path from s to t. Does the LP relaxation of the integer program you formulate always have an integer optimal solution? Why? 1. Formulate an integer program to find the shortest graph from node 1 to node 4 in Figure 1. Does Figure 1: A directed graph with four nodes (the number next to each arc is the arc length). the LP relaxation of your integer program have an integer optimal solution? Now consider a general directed graph G (N, A), where N is the set of nodes, A is the set of arcs, and cij is the length of arc (i,j) E A. Assume that c20 for each (i.j) A. Given two nodes s,te N, try to formulate an integer program to find the shortest path from s to t. Does the LP relaxation of the integer program you formulate always have an integer optimal solution? Why