Problem #3 (About Simplex tableaux, JBO, 3.4) [25 points] Consider the following simplex tableau (corresponding to a minimization problem): Table 2: Simplex tableau Z x1 x2 X3 x4 X5 x6 x7 1 0 -2 B 0 0 12 0 1 -2 -1 4 0 3 0 4 0 0 0 0 10 0 0 2 2 -3 5 1 0 0 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 , , y, d, e, and . 1. Under what conditions on 7 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, , and y is the current basic solution nondegenerate and optimal? 4. Assume that a, , Y, and satisfy the conditions of Part 3. Write at least one additional condition for the problem to have multiple optimal solutions. 5. Assume >0. Under what conditions on a, , and is the current basic solution optimal and the problem has a unique optimal solution? 6. Assume that a 0,