3. (Sensitivity Analysis) Consider the following linear programming problem: Maximize 1x1 + 2x2 Subject to X1 + *2 = 12 X256 X1,X2 2 0 Please get the answer and sensitivity reports using Excel. a. What is the optimal solution and the optimal objective function value? (2pt) b. If the objective function was changed to maximize 1x1 + 5x2 would the optimal solution of *1 = 6 and x2 = 6 change? If yes then what is the new optimal solution point? (2pt) c. If the objective function was changed to maximize 1x1 + 5x2 would the optimal objective function value of 18 change? If yes then what is the new optimal objective function value? (2pt) d. The shadow price of the original problem is 1 for constraint 1 so if the RHS current value of 12 is increased by one to 13 what is the effect if any on the current optimal objective function value of 18? (2pt) e. The shadow price of the original problem is 1 for constraint 1 so if the RHS current value of 12 is increased by 0.5 to 13.5 what is the effect if any on the current optimal objective function value of 18? (2pt) f. The shadow price of the original problem is 0 for constraint 2 so if the RHS current value of 8 is increased by one to 9 what is the effect if any on the current optimal objective function value of 18? (2pt) g. Which constraint of the original problem is binding, constraint 1 or 2 and why? (2pt)