Question 4 (20 points] Consider the following simplex tableau (corresponding to a minimization problem): Table: Simplex tableau L2 25 26 7 21 23 0 0 1 0 12 24 B 4 -2 -2 0 1 a -1 8 3 27 0 0 1 0 4 1 0 0 0 1 0 0 0 5 E 0 0 1 -3 n 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, , 7, 8, , and n. 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 y is the current basic solution nondegenerate and optimal? 4. Assume that a, B, 7, and n satisfy the conditions of Part 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 is the current basic solution optimal and the problem has a unique optimal solution? 6. Assume n > 0. Under what conditions on a and 8 can the simplex algorithm immediately end with a proof that the objective value is unbounded from below