The following table gives the travel costs between city pairs. Note that travel is allowed n either direction with the same travel cost. 1. Write a complete integer linear programming formulation of the Symmetric Travelling Salesman Problem for the given network. Clearly define the decision variables. With "complete" is meant that you should write the objective function and each individual constraint of the formulation with the given data substituted in the appropriate places. 2. Recall the Lagrangian relaxation of the Symmetric Travelling Salesman Problem covered in class. Choose node r=f as the special root node, and choose intitial penalty multipliers a=0,b=0,c=0,d=0,e=0. Write the Lagrangian relaxation of the Symmetric Travelling Salesman Problem covered in class for the given network. 3. Solve the Lagrangian relaxation of the Travelling Salesman Problem on the network using the method discussed in class. Neatly show your solution and objective value of the Lagrangian relaxation. Also, show your calculation of a lower bound for the optimal objective value of the TSP. 4. For each of the penalty multipliers i, determine the direction in which the penalty multiplier should be adjusted. Explain. 5. Next, adjust each of the penalty multipliers i by 3 in the appropriate direction. Write down the new values of the penalty multipliers i. The following table gives the travel costs between city pairs. Note that travel is allowed n either direction with the same travel cost. 1. Write a complete integer linear programming formulation of the Symmetric Travelling Salesman Problem for the given network. Clearly define the decision variables. With "complete" is meant that you should write the objective function and each individual constraint of the formulation with the given data substituted in the appropriate places. 2. Recall the Lagrangian relaxation of the Symmetric Travelling Salesman Problem covered in class. Choose node r=f as the special root node, and choose intitial penalty multipliers a=0,b=0,c=0,d=0,e=0. Write the Lagrangian relaxation of the Symmetric Travelling Salesman Problem covered in class for the given network. 3. Solve the Lagrangian relaxation of the Travelling Salesman Problem on the network using the method discussed in class. Neatly show your solution and objective value of the Lagrangian relaxation. Also, show your calculation of a lower bound for the optimal objective value of the TSP. 4. For each of the penalty multipliers i, determine the direction in which the penalty multiplier should be adjusted. Explain. 5. Next, adjust each of the penalty multipliers i by 3 in the appropriate direction. Write down the new values of the penalty multipliers i