1. (14pts) Consider the following problem. Maximize Z= 8x1 + 6x2 subject to X1 + 3x2 0, X2 > 0 Let y4 and yo be the surplus variables for the first and second constraints, respectively, in its dual problem. And let ys and y, be the corresponding artificial variables. After using the Big M method, the initial simplex tableau of its dual model ready to apply the simplex method is as follows: Basic W 1 Y2 Y3 94 ys yo Y RHS variable -1 -4M+2 -6M+3 -4M+2 M 0 M M 0 -14M W| 0 1 4 2 - 1 1 0 0 8 0 3 2 2 0 0 -1 1 6 y; After applying the simplex method, a portion of the final simplex tableau is as follows: Basic W y Y2 y4 Ys yo RHS variable W -1 M-0.5 M-0.5 y2 0 0.3 -0.1 y1 0 -0.2 0.4 (a) Based on the above tableau, use the fundamental insight to identify the missing numbers in the final simplex tableau. Please show your calculation steps. (5pts) (b) Identify the defining equations of the CPF solution corresponding to the optimal BF solution in the final simplex tableau. (4pts) (c) If we change the objective coefficients to [15 5] in the primal form, test the current solution for its feasibility and for optimality. If either test fails, find a new optimal solution to the primal model. (5pts)