“A small roadway project consists of the following activities:”

Activity	Duration (days)	Predecessor(s)
A	4	–
B	6	A
C	3	A
D	5	B, C
E	2	C
F	4	D, E

“Determine the critical path and total project duration using the Critical Path Method (CPM).”

Step 1: Compute early start (ES) and early finish (EF) for each activity.

$\mathrm{EF}=\mathrm{ES}+\mathrm{Duration}$

• A: ES = 0 → EF = 4
• B: ES = 4 → EF = 10
• C: ES = 4 → EF = 7
• D: ES = max(10, 7) = 10 → EF = 15
• E: ES = 7 → EF = 9
• F: ES = max(15, 9) = 15 → EF = 19

Step 2: Compute late finish (LF) and late start (LS).

$\mathrm{LS}=\mathrm{LF}-\mathrm{Duration}$

• F: LF = 19 → LS = 15
• D: LF = 15 → LS = 10
• E: LF = 15 → LS = 13
• B: LF = 10 → LS = 4
• C: LF = min(10, 13) = 10 → LS = 7
• A: LF = min(4, 7) = 4 → LS = 0

Step 3: Identify the critical path (zero float).

Activities with zero float: $ABDF$

Answer: Critical Path = A–B–D–F; Total Project Duration = 19 days.