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Consider a linear program with six variables 1,..., and three constraints. At an iteration of the Simplex method we have basic variables B = {09,46, e), non-basic variables N = {1,13,14}, transformed right hand side B-) = (3.7. 117, and objective function value B-16 = 25. Addi- tionally, we obtain the following information at the current basic fossible solution (BFS): -3 -1 23 -6 -1 - 1 0 1 Bla 3 1 Part 1. (10pt) Suppose that this linear program has a minimizing objective function. Do you think the current BFS is optimal? Pick one from the following three to continue. If you think the current BFS is optimal, explain why. (5pt) Additionally, find an alternative optimal BFS if there are any. (5pt) If you think the current BFS is not optimal and the problem is bounded, explain why, (5pt) Then, continue to use the Simplex pivot to derive an optimal solution to this problem. (5pt) Please present your steps clearly and specify at each iteration which variable to enter which to exit. . If you think the current BFS is not optimal and the problem is unbounded, explain why. (5pt) Additionally, provide an unbounded direction. (5pt) Part 2. (10pt) Regardless of the direction of optimization, do you think there exists a feasible solution that has an objective function value equaling to 12257 Pick one from the following two to continue . If you think such a feasible solution does not exist, explain why. (pt) Additionally, find a different solution such that ay > 0 for all y = 1,...,6.5pt) . If you think such a feasible solution exists, explain why. (5pt) Additionally, find this solution and show the cerivation you conduct. (pt) Consider a linear program with six variables 1,..., and three constraints. At an iteration of the Simplex method we have basic variables B = {09,46, e), non-basic variables N = {1,13,14}, transformed right hand side B-) = (3.7. 117, and objective function value B-16 = 25. Addi- tionally, we obtain the following information at the current basic fossible solution (BFS): -3 -1 23 -6 -1 - 1 0 1 Bla 3 1 Part 1. (10pt) Suppose that this linear program has a minimizing objective function. Do you think the current BFS is optimal? Pick one from the following three to continue. If you think the current BFS is optimal, explain why. (5pt) Additionally, find an alternative optimal BFS if there are any. (5pt) If you think the current BFS is not optimal and the problem is bounded, explain why, (5pt) Then, continue to use the Simplex pivot to derive an optimal solution to this problem. (5pt) Please present your steps clearly and specify at each iteration which variable to enter which to exit. . If you think the current BFS is not optimal and the problem is unbounded, explain why. (5pt) Additionally, provide an unbounded direction. (5pt) Part 2. (10pt) Regardless of the direction of optimization, do you think there exists a feasible solution that has an objective function value equaling to 12257 Pick one from the following two to continue . If you think such a feasible solution does not exist, explain why. (pt) Additionally, find a different solution such that ay > 0 for all y = 1,...,6.5pt) . If you think such a feasible solution exists, explain why. (5pt) Additionally, find this solution and show the cerivation you conduct. (pt)
