A+UM+ Question 1) Activity Predecessor Optimistic Most Pessimistic Likely A 5 7 15 B 14 21 22 C 21 33 45 D A 14 16 30 E B 18 19 26 F B 7 9 11 G B. C 7 9 17 D 8 8 8 I D, E 3 4 5 F. G 4 5 6 K H. I 7 8 21 a) (10 points) Develop an AOA diagram for the given activities. b) (5 points) Find the critical path and project completion time. c) (10 points) Find the probability of completing the project at 58 days. d) (10 points) The project manager is promised $12,000 if the project completed in less than 50 days, $8,000 if the project completed within 50-53 days, and no reward if the project goes above 53 days. What is the expected value of the manager's bonus?