A partially solved PERT problem is detailed in the table below. Times are given in weeks.
Activity 
Immediate Predecessor(s) 
Optimistic 
Most Likely 
Pessimistic 
A 
 
8 
10 
15 
B 
 
7 
8 
9 
C 
A 
5 
6 
10 
D 
A 
3 
3 
3 
E 
B,D 
1 
5 
9 
F 
B,D 
4 
7 
10 
G 
C 
3 
8 
10 
H 
E 
5 
7 
9 
I 
E 
4 
5 
8 
J 
F 
2 
5 
8 
K 
H, I 
1 
3 
6 
a) Calculate the expected duration (D), and variance of each activity.
b) Calculate ES, EF, LS, LF, S) for each activity.
ET 
Variance 
ES 
EF 
LS 
LF 
S 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 
c) Which activities form the critical path?
A) ADEHK
B) ACG
C) ABEK
D) ADEIK
E) BFJ
F) BEHK
d) What is the estimated time of the critical path? ( …… ) weeks 

e) If the project is due to be completed in 35 weeks, what is the probability that the project will be completed on the due date? ( … %) ? 

f) If the project manager wants at least a 95% probability that the project will be completed on the due date, what is the shortest project due date that will satisfy the manager? ( …… ) weeks 

g) Which activity (ies) can be delayed 1.67 weeks without impacting the expected project completion date? A) I B) A C) C D) F and G E) I and J


h) How many week(s) can you delay the activity J, without impacting the expected project completion date? ( ….. ) weeks 
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