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Consider the following problem. Minimize W=5y1 + 4y2, subject to 4y + 3y2 24 2y + y2 23 y + 2y2 2 1 y + y2 2 2 and Y1 20, Y220. Because this primal problem has more functional constraints than variables, suppose that the simplex method has been applied directly to its dual problem. If we let x5 and Xe denote the slack variables for this dual problem, the resulting final simplex tableau is Coefficient of: Basic Variable Right Side Eq. z X1 X2 X3 X4 X5 6 NAX X2 X4 (0) (1) (2) 1 0 0 3 1 2 0 1 0 2 -1 3 0 0 1 1 1 1 1 -1 2 9 1 3 For each of the following independent changes in the original primal model, you now are to conduct sensitivity analysis by directly investigating the effect on the dual problem and then inferring the complementary effect on the primal problem. For each change, apply the procedure for sensitivity analysis summarized at the end of Sec. 7.1 to the dual problem (do not reoptimize), and then give your conclusions as to whether the current basic solution for the primal problem still is feasible and whether it still is optimal. Then check your conclusions by a direct graphical analysis of the primal problem. (a) Change the objective function to W = 3/4 + 5y2. (b) Change the right-hand sides of the functional constraints to 3, 5, 2, and 3, respectively. (c) Change the first constraint to 291 + 4y2 27. (d) Change the second constraint to 5y1 + 2y2 2 10