A project has activities A (3 days), B (5 days), C (4 days), and D (2 days). The sequence is A→B→D and A→C→D. What is the critical path duration?
Correct Answer
C) 10 days
Path A→B→D = 3+5+2 = 10 days. Path A→C→D = 3+4+2 = 9 days. The critical path is the longest path at 10 days.
Why This Is the Correct Answer
The critical path is the longest sequence of activities that determines the minimum project duration. To find it, we calculate the total duration of each possible path through the network. Path A→B→D takes 10 days (3+5+2) while path A→C→D takes 9 days (3+4+2). Since 10 days is longer, it becomes the critical path and determines the project duration.
Why the Other Options Are Wrong
Option A: 11 days
This represents the duration of path A→C→D (3+4+2 = 9 days), which is the shorter path and therefore not the critical path.
Option D: 9 days
This would be the result if you incorrectly added only activities A, B, and C (3+5+4 = 12 days), but this doesn't represent any valid path through the network since B and C are parallel activities.
Memory Technique
Remember 'CRITICAL = LONGEST' - the critical path is always the path that takes the longest time to complete, just like the most critical bottleneck in any process.
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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