1- Consider an 8-node network (with 0 as the depot vertex and 7 other vertices) where the travel cost matrix and the demands are as follows: 0 6723 0 1 279 279 0 546 672 OORHEERSE 7 0 3 420 4 565 5 6 2 3 546 420 672 256 0 605 256 605 0 288 958 349 4 5 565 370 288 484 958 349 0 772 6 309 574 188 604 521 370 484 188 431 309 574 604 702 845 341 431 772 845 0 516 340 516 0 216 521 122 444 340 593 Using a homogeneous fleet of vehicles with capacity 100: a) Find the solution using the Nearest Neighbor heuristic. b) Find the solution using the Insertion heuristic. 7 341 702 122 56 216 1) Uncapacitated Facility Location problem (UFL) Use the model where Sij is the number of transferred units. 2) P-Median problem where we want to open exactly 3 facilities. 3) P-Center Problem where we want to open exactly 4 facilities. 444 593 0 Demand 5 30 105 40 35 30 25 20 c) Find the solution using the Clarke & Wright Savings heuristic. d) Using an exchange-neighborhood type algorithm where you exchange two vertices, try to improve your solution in (a) or show that it may not be improved. Note that you do not need to code the 18 question. You should show your work on paper to illustrate your understanding of how these heuristic methods work. 2- Formulate and solve the following problems using the data files which are provided. Work individually and report your answers clearly in a word file. Provide your codes and excel files as well. All the of the files should be compressed and submitted as a single file through