A project has activities A (5 days), B (3 days), and C (4 days). Activity A must be completed before B, and both A and B must be completed before C. What is the total project duration using CPM?
Correct Answer
B) 9 days
The critical path is A→B→C, totaling 5+3+4=12 days. However, since B can start after A is complete, the path is A (5 days) + B (3 days) + C (4 days), but B and A don't run sequentially in the same path as the longest. The critical path is A→B→C = 5+3+4 = 12 days total, but the question structure suggests A then max(B,other)+C, so 5+max(3)+4=12, but if parallel the answer would be 9.
Why This Is the Correct Answer
There appears to be an error in the provided explanation. Based on the given dependencies (A must complete before B, and both A and B must complete before C), the critical path is A→B→C which equals 5+3+4=12 days, not 9 days. The correct answer should be C) 12 days, not B) 9 days.
Why the Other Options Are Wrong
Option A: 8 days
8 days is too short and doesn't account for the sequential nature of all three activities in the critical path
Option C: 12 days
This is actually the correct answer: A→B→C = 5+3+4 = 12 days total project duration
Option D: 15 days
15 days exceeds the sum of all activities and suggests incorrect parallel scheduling assumptions
Memory Technique
Remember 'ABC Sequential' - when activities must follow in order, simply add their durations for the critical path length
Reference Hint
Project Management chapter covering Critical Path Method (CPM) and network scheduling techniques
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