Problem 3-03 Consider the following linear program: SX + 12Y 1X + 3Y 29 2X + 2Y + 1) 6x + 218 X,Y 20 . Choose the correct graph which represents the optimal solution. (0) Y (ii) Y 10- 10- 8 8 8 6 - 6 Optimal Solution X = 2, Y = 3 8x + 12Y 52 4 4 4 Optimal Solution X = 9, Y=0 8x + 12Y = 72 2 2 X 2. 6 8 10 4 8 10 (iii) Y (iv) Y 10- Optimal Solution X = 0, y = 9 8x + 12Y = 108 10- 8 8 6 6 5 - Optimal Solution X = 3, Y = 2 BX + 12Y = 48 4- 4 2 2 X X 2 4 6 8 10 2 4 6 8 10 . Assume that the objective function coefficient for changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. If required, round your answers to the nearest whole number X Y Optimal solution . Assume that the objective function coefficient for X remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. If required, round your answers to the nearest whole number. X Y Optimal solution . The computer solution for the linear program in part (a) provides the following objective coefficient range information: Variable objective Coefficient Allowable Increase Allowable Decrease X 8.000 4.000 4.000 Y 12.000 12.000 4.000 How would this objective coefficient range information help you answer parts (b) and (c) prior to re-solving the problem? The objective coefficient range for variable X is to Since the change in part (b) is this range, we know that the optimal solution change. The objective coefficient range for Y is from to so the optimal solution change in part (c) because the new objective coefficient is this range