18 In Exercise 16, suppose that the estimates

(a, b,m) are given in Table 16 and that activity times follow a beta distribution. Use the data in the table to calculate the expected activity times, and then compute the critical path for each event using as the completion time for activity (i, j). Assume that the solution that you obtain is the “planned” time to complete each event, and then find the probabilities that the events will occur without delay.

TABLE 16 Project (a)
Activity

(a,

b, m) Activity

(a,

b, m)
1, 2 (5, 8, 6) 3, 6 (3, 5, 4)
1, 4 (1, 4, 3) 4, 6 (4, 10, 8)
1, 5 (2, 5, 4) 4, 7 (5, 8, 6)
2, 3 (4, 6, 5) 5, 6 (9, 15, 10)
2, 5 (7, 10, 8) 5, 7 (4, 8, 6)
2, 6 (8, 13, 9) 6, 7 (3, 5, 4)
3, 4 (5, 10, 9)
Project (b)
Activity

(a,

b, m) Activity

(a,

b, m)
1, 2 (1, 4, 3) 3, 7 (12, 14, 13)
1, 3 (5, 8, 7) 4, 5 (10, 15, 12)
1, 4 (6, 9, 7) 4, 7 (8, 12, 10)
1, 6 (1, 3, 2) 5, 6 (7, 11, 8)
2, 3 (3, 5, 4) 5, 7 (2, 8, 4)
2, 5 (7, 9, 8) 6, 7 (5, 7, 6)
3, 4 (10, 20, 15)