DI 7.2-4. Consider the following problem. Maximize Z = 2x1 + 7x2 3x3, subject to X1 + 3x2 + 4x3 = 30 x1 + 4x2 x3 = 10 and X1 20 x2 = 0, X3 20. By letting x4 and x5 be the slack variables for the respective con- straints, the simplex method yields the following final set of equations: (0) (1) (2) z + x2 + x3 + 2x5 = 20 X2 + 5x3 + x4 x1 + 4x2 - X3 + x3 = 10. X5 = 20 Now you are to conduct sensitivity analysis by independently in- vestigating 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 eval- uating the current basic solution. Then test this solution for fea- sibility and for optimality. If either test fails, reoptimize to find a new optimal solution. (a) Change the right-hand sides to b 1) = 20 [30] b2 (b) Change the coefficients of xz to C3 2 013 | -2] 023- (c) Change the coefficients of xy to C1 4 011 3 021. 2 (d) Introduce a new variable x with coefficients C6 -3 016 1 26. 2 (e) Change the objective function to Z = x1 + 5x2 2x3. (f) Introduce a new constraint 3x1 + 2x2 + 3x3 = 25. (g) Change constraint 2 to x + 2x2 + 2x3 = 35