A project has activities with the following durations and dependencies: A(5 days), B(3 days, after A), C(7 days, after A), D(4 days, after B and C). What is the critical path duration?
Correct Answer
A) 16 days
The critical path is A→C→D (5+7+4=16 days) since path A→B→D only takes 12 days (5+3+4). The longest path determines the project duration.
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 must calculate all possible paths from start to finish and identify the one with the greatest total duration. Path A→C→D takes 16 days (5+7+4), while path A→B→D takes only 12 days (5+3+4), making A→C→D the critical path at 16 days.
Why the Other Options Are Wrong
Option C: 14 days
12 days represents the duration of the shorter path A→B→D (5+3+4=12), not the critical path which must be the longest path through the network
Option D: 19 days
19 days would result from incorrectly adding all activity durations (5+3+7+4=19) without considering that activities B and C occur simultaneously after A, not sequentially
Memory Technique
Remember 'CRITICAL = LONGEST' - the critical path is always the path that takes the most time, creating the bottleneck for your entire project schedule
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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