Question 2 (Integer linear programming: 10 marks) The TRAVELLING SALESMAN problenm (TSP) is a classical NP-hard problem. The input is a complete graph G with vertex set V and a weight function w : V V R assigning a weight w(u, v) to every edge (u, v) in G. The goal is to find a cycle in G that visits every vertex exactly once and such that the total weight of the edges in the cycle is minimized. Express this problem as an integer linear program and argue that an optimal solution to the ILP you provide corresponds to an optimal solution to the TSP Question 2 (Integer linear programming: 10 marks) The TRAVELLING SALESMAN problenm (TSP) is a classical NP-hard problem. The input is a complete graph G with vertex set V and a weight function w : V V R assigning a weight w(u, v) to every edge (u, v) in G. The goal is to find a cycle in G that visits every vertex exactly once and such that the total weight of the edges in the cycle is minimized. Express this problem as an integer linear program and argue that an optimal solution to the ILP you provide corresponds to an optimal solution to the TSP