The manager of the Oak Hills Swimming Club is planning the club’s swimming team program. The first team practice is scheduled for May 1. The activities, their immediate predecessors, and the activity time estimates (in weeks) are as follows: Activity OptimisticMost Probable PessimisticImmediate PredecessorsA123-B468AC246AD123B, CE234BF123AG123DH123GI111E, H, F A. Draw a project network for this problem. B. Fill in all the blanks in the following table. Note: For variance (σ2) in activity time, keep two decimal places. ActivityExpected Time t (weeks)Variance σ2 ES EF LS LF SlackCriticalPath?A B C D E F G H I

Project network is the graphical representation of project activities and their duration to complete the project. The project network for the problem is as follows: 2. The calculation for activity duration is as follows: The calculation for variance is as follows: The early start of activity A will be zero and the early start of other activities is the early finish of the previous activity. The calculation for the early finish is as follows: The late finish of activity I is the same as the early finish of the same. The late finish of other activities is the late start of the previous activity. Therefore, the calculation for the late start is as follows: There are four paths available in the network. They are the following: A > B > E > I = 2 + 6 + 4 + 1 = 13 weeks A > B > D > G > H > I = 2 + 6 + 2 + 2 + 2 + 1 = 15 weeks A > C > D > G > H > I = 2 + 4 + 2 + 2 + 2 + 1 = 13 weeks A > F > I = 2 + 2 + 1 = 5 weeks The critical path is the longest path of the network, i.e., the path that takes the highest time to complete the project. Therefore, the critical path is A > B > D > G > H > I with a project duration of 15 weeks. The calculation for the total slack of critical paths is as follows: The activity table is as follows: Activity Expected Duration Variance ES EF LS LF Critical slack path A 2 0.11 0 2 0 2 0 B 6 0.44 2 8 2 8 0 C 4 0.44 2 6 4 8 D 2 0.11 8 10 8 10 0 E 4 0.11 8 12 10 14 F 2 0.11 2 4 12 14 G 2 0.11 10 12 10 12 0 H 2 0.11 12 14 12 14 0 I 1 0 14 15 14 15 0