14 2.Consider a project with activities and their optimistic, most likely and pessimistic completion times (in days) given below: Activity Preceding Optimistic Most Pessimistic Activity Likely A None 4 13 16 B None 8 None 13 31 D B 4 16 E A 19 57 F C,D 9 15 21 G E,F 13 H B 14 22 30 CD 24 36 48 J 14 24 34 20 19 28 23 ALOIS 18 23 NA (a) Using PERT estimate the expected completion time and its standard deviation for each of the above activities. (2 marks) (b) Using the activity on arrow approach, draw the network indicating clearly the critical path and the expected completion time of the project. (10 marks) (c) Determine the probabilities that each path through the network will be completed in 61 days? (8 marks) (d) What must the most likely activity time for B (answer to the nearest day) be adjusted to if the probability of any path through the network being completed in 69 days must not be less than 0.94? Indicate any practical contradictions (if any) that may occur from your answer. Has the critical path changed and if so to what? (30 marks)