Consider the following linear programming (LP) problem. Maximize Z=-5X1 + 5 x2 + 13 X3 subject to: -1 X1 + 1 x2 + 3x3 s 20 12 X1 + 4 x2 + 10 X3 s 90 X120, X220, X32 0. a. Construct the augmented form of this LP by introducing slack variables. (15 pts) b. The final simplex tableau for the above LP is given below. Basic Variable Coefficient of: Right Side Z X1 X2 X3 X4 X5 Z 1 0 0 2 5 0 100 Eq (0) (1) (2) X2 0 -1 1 3 1 0 20 XS 0 16 0 -2 -4 1 10 Now suppose that the right-hand side of the second constraint is changed from b2 = 90 to b2 = 70. Using the sensitivity analysis procedure covered in class, explain why the current solution is not optimal. Construct the revised tableau and provide the next step to follow (should primal simplex or dual simplex method be used to find the optimal solution?) (35 pts) c. Following the method you identified in part b), find the optimal solution and the optimal value for the revised problem. Provide also the revised final tableau. (50 pts)