1. **State the problem:** We need to find the critical path in a project network given tasks, their predecessors, and durations. 2. **List tasks and durations:** - A: 4 (no predecessor) - B: 7 (predecessor A) - C: 5 (predecessor A) - D: 8 (predecessor B) - E: 9 (predecessors B, C) - F: 3 (predecessors D, E) 3. **Identify all possible paths from start to finish:** - Path 1: A → B → D → F - Path 2: A → B → E → F - Path 3: A → C → E → F - Path 4: A → C → D → F (Note: D depends on B, so this path is invalid because C does not lead to D) 4. **Calculate total duration for each valid path:** - Path 1: $4 + 7 + 8 + 3 = 22$ - Path 2: $4 + 7 + 9 + 3 = 23$ - Path 3: $4 + 5 + 9 + 3 = 21$ 5. **Determine the critical path:** The critical path is the longest duration path, which is Path 2 with duration 23. 6. **Conclusion:** The critical path is **A, B, E, F**. **Final answer:** b. Path 2: A, B, E, F