Consider the following linear program: Max 3A + 2B s.t. 1A + 1B S 12 3A + 1B S 24 1A + 2B S 16 A, B 20 a. Choose the correct graph which represents the optimal solution. D (ii) B 26+ 24 221 20-1 18+ 16 14 B 26+ 24 22 201 18+ 16- 14 12 104 8- 6 20 12 10- Optimal Solution A = 6.4, B = 4.8 3A - 2B = 28.8 Optimal Solution A = 8, B = 4 3A + 2B = 32 61 1 2 2 + 6 S 10 12 14 16 18 20 LA $ 10 12 14 16 18 20 (1) B 26 (iv) 22 20 18 16 14 Optimal Solution . 1013A - 2B = 24 B 26 24 22 20 18 16 14 12 10 Graph (0) b. Assume that the objective function coefficient for A changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. The same extreme point remains optimal If required, round your answers to one decimal place. A 6.4 B 4.8 Optimal solution C. Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 7. Does the optimal solution change? Use the graphical solution procedure to find the new A new extreme point becomes optimal If required, round your answers to one decimal place. Optimal solution d. The sensitivity report for the linear program in part (a) provides the following objective coefficient range information: Variable Objective Coefficient 3.00000 2.00000 Allowable Increase 3.00000 4.00000 Allowable Decrease 2.00000 1.00000 A Use this objective coefficient range information to answer parts (b) and (c). The objective coefficient range for A is from 1 to 6 so the optimal solution will not change in part (b) because the new objective coefficient is in this range. The objective coefficient range for B is from 1 to 6 so the optimal solution will change in part (c) because the new objective coefficient is not in this range