1. **Problem Statement:** We have a list of activities with their durations and dependencies. We need to draw a network diagram, identify the critical path, and find the minimum project completion time. 2. **Understanding the Problem:** Each activity depends on one or more preceding activities. The network diagram shows these dependencies as arrows. 3. **List of Activities and Dependencies:** - A: 3 weeks, no predecessor - B: 5 weeks, preceded by A - C: 7 weeks, preceded by A - D: 6 weeks, preceded by B - E: 8 weeks, preceded by B - F: 3 weeks, preceded by C and D - G: 2 weeks, preceded by E and F 4. **Drawing the Network Diagram:** - Start with A. - B and C start after A. - D and E start after B. - F starts after both C and D. - G starts after both E and F. 5. **Calculating Earliest Start and Finish Times:** - A: starts at 0, finishes at $0 + 3 = 3$ - B: starts at 3, finishes at $3 + 5 = 8$ - C: starts at 3, finishes at $3 + 7 = 10$ - D: starts at 8, finishes at $8 + 6 = 14$ - E: starts at 8, finishes at $8 + 8 = 16$ - F: starts after max(C,D) finishes, so after max(10,14) = 14, finishes at $14 + 3 = 17$ - G: starts after max(E,F) finishes, so after max(16,17) = 17, finishes at $17 + 2 = 19$ 6. **Identifying the Critical Path:** - The critical path is the longest path through the network. - Paths and durations: - A-B-D-F-G: $3 + 5 + 6 + 3 + 2 = 19$ - A-B-E-G: $3 + 5 + 8 + 2 = 18$ - A-C-F-G: $3 + 7 + 3 + 2 = 15$ - The critical path is A-B-D-F-G. 7. **Minimum Project Completion Time:** - The project completes when the last activity on the critical path finishes. - Minimum completion time is 19 weeks. **Final answers:** - (a) Network diagram as described. - (b) Critical path: A-B-D-F-G (bold lines). - (c) Minimum project completion time: 19 weeks.