Question 2: (20 points) (This question can be solved in 20 minutes easily) Assume that we got the following Simplex Table while we were solving an LP model by the Simplex Algorithm. Does the following Simplex Table show the optimal solution? If it does not show the optimal solution continue to search by the Simplex Algorithm until finding the answer. At the end write the values of all the decision variables and objective function if you end up with an optimal solution. If you do not end up with an optimal solution write your conclusion: infeasible solution or unbounded solution. Basis X4 X2 0 X6 5 X7 0 0 X1 6 2 1 2 X3 -1 -2 1 Masz X7 X2 X4 0 3 X5 -6 -4 1 2 0 0 1 1 0 RHS 21 20 8 30 1 0 0 1 - 1 Question 3: (20 points) (This question can be solved in 20 minutes easily)Suppose that we have 5 jobs (1, 2, 3, 4, 5) waiting for being performed and 5 machines (A, B, C, D, E) that can be used to perform these jobs. The assignment costs of the jobs to the machines are given in the following table. Find the minimum total cost one-to-one assignment between the jobs and the machines by the Hungarian Method. At the end, write your solution clearly which job is assigned to which machine and what is the total cost in your solution? (Please give numbers to your tables like Table 1, Table2, ... in order to make it easier to follow your solution) B C D E 1 11 2 3 6 2 2 11 13 11 31 10 11 12 5 1 18 4 7 10 38 137 A 4 5 Question 4: (20 points) (This question can be solved in 20 minutes easily) A manufacturer has 4 depots and retailers all in different cities. Capacities of the depots, demands of the retailers, unit transportation costs from the depots to the retailers and an initial basic feasible solution are given in the following table. Use the given solution as your initial basic feasible solution and find the optimal solution by the Transportation Simplex Algorithm. Retailer 1 Retailer 2 Retailer 3 Retailer 4 Retailers Capacity 10 10 12 Depot 1 55 7 5 6 5 12 Depot 2 65 20 25 10 5 11 10 Depot 3 12 60 6 45 12 13 13 10 10 8 10 Depot 4 45 50 Demand