Consider the following linear programming problem: Min A + 2B s.t. A+ 4B S 21 B27 2A + 3A + 1.5B S 21 -2A + 6B 0 A, B 20 a. Select the correct graph that shows the optimal solution for the problem. (1) AB (ii) AB Optimal Solution A=1, B= A+2B=11 6- 5- 4- 3- Optimal Solution A=3, B=1 A+2B=5 2- 2- 1- 1- 0 (iii) (iv) AB 8- 6- 5. 5- - 4- 4- 3- 3- Optimal Solution A-6, B=2 A+2B=10 2- 2 Optimal Solution A=3.5, B=0 A+2B=3.5 0 Graph (0) b. Determine the amount of slack or surplus for each constraint. If an amount is zero, enter "O". If required, round your answers to one decimal place. (1) A + 4B 21 (2) 2A + B 2 7 (3) 3A + 1.5B 21 (4) -2A + 6B 2 0 b. Determine the amount of slack or surplus for each constraint. If an amount is zero, enter "0". If required, round your answers to one decimal place. (1) A + 48 5 21 (2) 2A + B 27 (3) 3A + 1.5B 21 (4) -2A + 68 20 c. Suppose the objective function is changed to Max 5A + 2B. Select the correct graph that shows the optimal solution for the problem. (1) AB (ii) Optimal Solution A=1, B=5 5A+2B=15 6- 4- 3- 2- Optimal Solution A=3.5, B=0 SA+2B=17.5 03 (iv) 6- 4- 4 3- 3- Optimal Solution A=6, B=2 5A+2B=34 Optimal Solution A-3. B=L SA+2B=17 1 2- 1- 1