Question 2 (50pts) Given the model: Maximization Coefficient of variables Sign RHS X1 X2 X3 Equation Objective function 9 8 5 Constraint 1 2 3 1 9 Constraint 2 5 4 3 11 X1, X2, X3 are nonnegative variables Given the solved final simplex tableau: Coefficient of: Basic Variables RHS X1 X2 X3 s1 s2 z 1 0 1 0 2 22 s1 -1 3/4 0 -1 1/4 1 - 3/4 3/4 X2 1 1/4 1 3/4 0 1/4 2 3/4 (Note: The number is in mixed number form) a. Show your algebraic steps to find the allowable range of the coefficient of variables 9 in the objective function so that the current optimal solution does not change. (30pts) b. Now, supposed that in the final tableau, the increase amount Ac in term of 6 for each coefficient of variable in row 0 is as follow: Ac = [0 200 0 - - 0] For 0>0, give the range of value of 0 for which this solution is both feasible and optimal. Use this tableau to identify the current basic solution as a function of 0. What is the best choice of 0 within this range? (20pts) Question 2 (50pts) Given the model: Maximization Coefficient of variables Sign RHS X1 X2 X3 Equation Objective function 9 8 5 Constraint 1 2 3 1 9 Constraint 2 5 4 3 11 X1, X2, X3 are nonnegative variables Given the solved final simplex tableau: Coefficient of: Basic Variables RHS X1 X2 X3 s1 s2 z 1 0 1 0 2 22 s1 -1 3/4 0 -1 1/4 1 - 3/4 3/4 X2 1 1/4 1 3/4 0 1/4 2 3/4 (Note: The number is in mixed number form) a. Show your algebraic steps to find the allowable range of the coefficient of variables 9 in the objective function so that the current optimal solution does not change. (30pts) b. Now, supposed that in the final tableau, the increase amount Ac in term of 6 for each coefficient of variable in row 0 is as follow: Ac = [0 200 0 - - 0] For 0>0, give the range of value of 0 for which this solution is both feasible and optimal. Use this tableau to identify the current basic solution as a function of 0. What is the best choice of 0 within this range? (20pts)