3. Consider the following linear program: 2. Consider the linear program in Problem 1. The value of the optimal solution is 27. Sup- pose that the right-hand side for constraint I is increased from 10 to 11. 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 I provides the following right- hand-side range information: Min 8X + 12Y S.T. 1X + 3Y 29 2X + 2Y =10 6X + 2Y =18 X, Y 20 Constraint a. b. 1 Constraint R.H. Side 10.000 24.000 16.000 Allowable Increase 1.200 6.000 Infinite Allowable Decrease 2.000 6.000 3.000 3 c. Use the graphical solution procedure to find the optimal solution. 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: What does the right-hand-side range information for constraint I tell you about the shadow price for constraint I? Variable d. The shadow price for constraint 2 is 0.5. Using this shadow price and the right-hand-side range information in part (c), what conclusion can you draw about the effect of changes to the right-hand side of constraint 2? Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 Y How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the problem? 3. Consider the following linear program: 2. Consider the linear program in Problem 1. The value of the optimal solution is 27. Sup- pose that the right-hand side for constraint I is increased from 10 to 11. 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 I provides the following right- hand-side range information: Min 8X + 12Y S.T. 1X + 3Y 29 2X + 2Y =10 6X + 2Y =18 X, Y 20 Constraint a. b. 1 Constraint R.H. Side 10.000 24.000 16.000 Allowable Increase 1.200 6.000 Infinite Allowable Decrease 2.000 6.000 3.000 3 c. Use the graphical solution procedure to find the optimal solution. 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: What does the right-hand-side range information for constraint I tell you about the shadow price for constraint I? Variable d. The shadow price for constraint 2 is 0.5. Using this shadow price and the right-hand-side range information in part (c), what conclusion can you draw about the effect of changes to the right-hand side of constraint 2? Objective Coefficient 8.000 12.000 Allowable Increase 4.000 12.000 Allowable Decrease 4.000 4.000 Y How would this objective coefficient range information help you answer parts (b) and (c) prior to resolving the