Consider the following problem. Maximize Z= 2x1 + 7X2 - 3X3, subject to Xy + 3x2 + 4xz s 30 Xy + 4x2 - X3 s 10 and X1 s 0, X220, X3 20. By letting X4 and X, be the slack variables for the respective constraints, the simplex method yields the following final set of equations: (0) (1) (2) Z + x2 + x3 + 2xs = 20 x2 + 5x3 + x4 - x = 20 x + 4x2 - X3 x's = 10. + Now you are to conduct sensitivity analysis by independently investigating each of the following seven changes in the original model. For each change, use the sensitivity analysis procedure to revise this set of equations in tableau form) and convert it to proper form from Gaussian elimination for identifying and evaluating the current basic solution. Then test this solution for feasibility and for optimality. If either test fails, reoptimize d a new optimal solution. (a) Change the right-hand sides to (s.) [30) (b) Change the coefficients of Xz to C3 a13 = 3 023_ (c) Change the coefficients of X, to 4 011 3 2 azi (d) Introduce a new variable xa with coefficients 20 016 026 (e) Change the objective function to Z = xy + 5x2 - 2X3. (f) Introduce a new constraint 3x1 + 2x2 + 3x3 s 25. (9) Change constraint 2 to X1 + 2X2 + 2Xz s 35