Quiz 6 – Question 1 (CPM / ES-EF / LS-LF / Slack Solution)
Given Activities
a: 5 days (start)
b: 3 days (start)
c: 2 days (after a)
d: 3 days (after b)
e: 7 days (after c and d)
(a) Network Diagram (Precedence Relationships)
Start → a(5) → c(2) → e(7) → Finish
Start → b(3) → d(3) → e(7) → Finish
(b) Paths and Critical Path
Path 1: a → c → e = 5 + 2 + 7 = 14 days
Path 2: b → d → e = 3 + 3 + 7 = 13 days
Critical Path = a → c → e (longest path)
(c) ES/EF/LS/LF and Slack
Forward Pass (ES/EF), start time = 0:
a: ES=0, EF=5
b: ES=0, EF=3
c (after a): ES=5, EF=7
d (after b): ES=3, EF=6
e (after c and d): ES=max(7,6)=7, EF=14
Project duration (normal) = 14 days
Backward Pass (LS/LF), set LF of final activity e = 14:
e: LF=14, LS=7
c: LF=7, LS=5
d: LF=7, LS=4
a: LF=5, LS=0
b: LF=4, LS=1
Slack = LS − ES (or LF − EF):
Activity
Duration
ES
EF
LS
LF
Slack
a
5
0
5
0
5
0
b
3
0
3
1
4
1
c
2
5
7
5
7
0
d
3
3
6
4
7
1
e
7
7
14
7
14
0
Critical activities (0 slack): a, c, e
(d) Project Duration
Project duration = 14 days