A project has activities with the following durations and dependencies: Activity A (5 days), Activity B (3 days, depends on A), Activity C (4 days, depends on A), Activity D (2 days, depends on B and C). What is the critical path duration?
Correct Answer
A) 11 days
The critical path is A→C→D (5+4+2=11 days) or A→B→D (5+3+2=10 days). Since C takes longer than B, the critical path duration is 11 days through A→C→D.
Why This Is the Correct Answer
The critical path is the longest sequence of dependent activities that determines the minimum project duration. To find it, we calculate all possible paths from start to finish and identify the one with the greatest total duration. Path A→C→D totals 11 days (5+4+2), while path A→B→D totals 10 days (5+3+2), making A→C→D the critical path at 11 days.
Why the Other Options Are Wrong
Option B: 12 days
12 days is incorrect because it doesn't represent any valid path through the network. The longest possible path is A→C→D at 11 days, so 12 days exceeds the actual critical path duration.
Option C: 14 days
14 days is incorrect because it appears to add all activity durations (5+3+4+2=14), but this ignores the network logic where activities B and C run in parallel after A, not sequentially.
Option D: 9 days
9 days is incorrect because it's less than both possible paths through the network. This might result from miscalculating one of the paths or forgetting to include all required activities in the sequence.
Memory Technique
Remember 'LONGEST = CRITICAL' - the critical path is always the longest duration path through your project network, not the shortest or most convenient route.
Reference Hint
Look up 'Critical Path Method (CPM)' or 'Project Scheduling' in construction management chapters, typically found in project management or scheduling sections
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