The following table shows the activities their optimistic, most likely and pessi

Question

The following table shows the activities their optimistic, most likely and pessimistic durations and their immediate predecessors

Activity a   m b Immediate Predecessors

A 4 8 12 ---

B 4 10 13 A

C 7 14 18 B

D 9 16 20 B

E 6 9 12 B

F 2 4 6 D,E

G 4 7 13 C,F

H 3 5 7 G

I 2 3 4 G,H

A- Determine the expected times and variances for each activity

B- Construct a project network for this problem

C- What is the probability that the project will be finished in less than 57 days?

D- What is the probability that the project will need at least 50 days?

Explanation / Answer

Expected time and varience for activiy A

a = 4 m =8 b =12

Expected time = (a+4m+b)/6 = (4+4*8+12)/6 = 8

Varience = (b-a)/6 = (12-4)/6 = 1.33

Total project duration,

0.33333

Taking all this values in network diagram,

critical path will be,

A-B-C-G-H-I

Project Duration = 8+9.5+13.5+7.5+5+3 = 46.5

Varience of project = sqrt(Va^2 + Vb^2 + Vc^2 + Vg^2 + Vh^2 + Vi^2)

V = sqrt(10.19)

V = 3.19

P(x<57) = P(z< (57-46.5)/3.19 )

P(x<57) = P(z< 3.29)

P(x<57) = 0.9995

P(x>50) = 1 - P(x<50)

P(x>50) = 1 - P(z<(50-46.5)/3.19)

P(x>50) = 1 - P(z<1.09)

P(x>50) = 1 - 0.8621

P(x>50) = 0.1379

a m b E V A 4 8 12 8 1.33333 B 4 10 13 9.5 1.5 C 7 14 18 13.5 1.83333 D 9 16 12 14.16667 0.5 E 6 9 12 9 1 F 2 4 6 4 0.66667 G 4 7 13 7.5 1.5 H 3 5 7 5 0.66667 I 2 3 4 3

0.33333

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