https://file.aiquickdraw.com/mathbot/file/1726486953657p5aic07q.jpg

To identify the critical path, we need to analyze the activity network for this project based on the precedence table and durations provided. Here is a breakdown of the steps to determine the critical paths and their durations:

### **1. Listing the Activities and Dependencies:**
The given table shows:
- **A**: Duration = 2 months, No predecessor.
- **B**: Duration = 7 months, No predecessor.
- **C**: Duration = 3 months, Predecessor = A.
- **D**: Duration = 6 months, Predecessor = A.
- **E**: Duration = 8 months, Predecessor = B.
- **F**: Duration = 4 months, Predecessor = B.
- **G**: Duration = 3 months, Predecessor = C.
- **H**: Duration = 7 months, Predecessors = D, E.

### **2. Finding Paths and Their Durations:**
We need to identify all possible paths from the start to the end of the project and sum up the durations of activities in each path:

- **Path 1:** A → C → G
  - Duration = 2 (A) + 3 (C) + 3 (G) = 8 months.

- **Path 2:** A → D → H
  - Duration = 2 (A) + 6 (D) + 7 (H) = 15 months.

- **Path 3:** B → E → H
  - Duration = 7 (B) + 8 (E) + 7 (H) = 22 months.

- **Path 4:** B → F
  - Duration = 7 (B) + 4 (F) = 11 months.

### **3. Identifying the Critical Path:**
The critical path is the one with the longest duration, which determines the project's minimum completion time.

- **Critical Path:** B → E → H with a total duration of 22 months.

### **4. Additional Notes:**
- The handwritten note on the image mentions two paths: "A-D-E-G-H-K" and "C-F-I-L." However, based on the table, the information does not match these exact paths, possibly indicating a misunderstanding or typo. The critical path analysis based on the provided data concludes with the path identified above.

Would you like more details or have any questions about this analysis?

### **Related Questions:**
1. What is the significance of identifying the critical path in project management?
2. How do delays in activities on the critical path affect the overall project timeline?
3. What techniques can be used to shorten the duration of the critical path?
4. Can there be more than one critical path in a project? If so, how would that affect project management?
5. How do "float" or "slack" times influence the scheduling of non-critical path activities?

### **Tip:**  
When sketching an activity network, use nodes for activities and arrows to indicate dependencies, which helps visualize the critical path and dependencies.

Identify the Critical Path based on the given activity network and precedence table.

Analyze a project's critical path by calculating the longest duration path based on activity dependencies. Learn how to determine critical paths and how they impact project timelines, with detailed calculations based on the provided activity table.

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