3. Consider the following linear program: Min 8X+12Y s.t. 1X3Y9 2X+2Y10 6X + 2Y18 X, Y0 a. Use the graphical solution procedure to find the optimal solution. b. c. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new opti- mal solution. Assume that the objective function coefficient for X remains 8, but the objective func- tion coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d. The sensitivity report for the linear program in part (a) provides the following objec- tive coefficient range information: Variable Objective Coefficient Allowable Increase Allowable Decrease X Y 8.000 12.000 4.000 12.000 4.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem? 4. Consider the linear program in Problem 3. The value of the optimal solution is 48. Sup- pose that the right-hand side for constraint 1 is increased from 9 to 10. a. Use the graphical solution procedure to find the new optimal solution. b. Use the solution to part (a) to determine the shadow price for constraint 1. c. The sensitivity report for the linear program in Problem 3 provides the following right- hand-side range information: Constraint Allowable Allowable Constraint R.H. Side Increase Decrease 1 9.000 2.000 4.000 2 10.000 8.000 1.000 3 18.000 4.000 Infinite