Question #4: About Simplex tableaux (30 points) Consider the following simplex tableau (corresponding to a minimization problem): 2 23 1 0 0 0 T1 0 1 0 0 Table 2: Simplex tableau 22 14 25 26 -2 a B 0 7 -2 -1 4 0 1 0 8 0 0 E 1 -3 5 1 0 27 0 0 1 0 8 4 2 77 All parts refer to the basic solution for the above tableau. In each case, give the most general answer possible; conditions should be as succinct and necessary as possible. In each case express the answer in terms of equalities or inequalities involving one or more of the terms of a, 8, 7, 8, E, and 11. 1. Under what conditions on n is the current basic solution feasible and nondegenerate? 2. Under what conditions on n is the current basic solution feasible and degenerate? 3. Under what conditions on a, b, and is the current basic solution optimal? 4. Assume that a, B, 7, and 11 satisfy the conditions of Parts 1 and 3. Write at least one additional condition for the problem to have multiple optimal solutions. 5. Assume n > 0. Under what conditions on a, b, and y is the current basic solution optimal and the problem has a unique optimal solution? 6. Assume that a 0. Under what conditions on y and e is Xe the entering variable and 27 the leaving variable in an improving simplex pivot (one in which a better solution is produced)