The image you've provided appears to depict a project network diagram, commonly used for Critical Path Method (CPM) analysis. Each node seems to represent a task, and the arrows indicate dependencies with numbers representing the task duration in some form (likely days).

To find the critical paths, we need to:

1. Identify all the paths from the starting node to the ending node.
2. Add up the durations along each path.
3. Identify the paths with the longest durations, as these are the critical paths (i.e., the paths where any delay would impact the project's overall duration).

Let’s analyze the network by examining the paths:

Paths in the network:

• Path 1: $A \rightarrow D \rightarrow H \rightarrow I \rightarrow J$

  • Durations: $6 + 4 + 2 + 7 + 12 = 31$

• Path 2: $A \rightarrow D \rightarrow F \rightarrow I \rightarrow J$

  • Durations: $6 + 4 + 2 + 7 + 12 = 31$

• Path 3: $A \rightarrow E \rightarrow F \rightarrow I \rightarrow J$

  • Durations: $6 + 2 + 2 + 7 + 12 = 29$

• Path 4: $B \rightarrow G \rightarrow K \rightarrow J$

  • Durations: $4 + 4 + 8 + 12 = 28$

• Path 5: $C \rightarrow G \rightarrow K \rightarrow J$

  • Durations: $4 + 4 + 8 + 12 = 28$

Critical Paths:

The two longest paths are:

• $A \rightarrow D \rightarrow H \rightarrow I \rightarrow J$ with a total duration of 31 units.
• $A \rightarrow D \rightarrow F \rightarrow I \rightarrow J$ with a total duration of 31 units.

Both of these paths have the same longest duration, making them the critical paths.

Do you want further details on how to calculate slack time for non-critical paths or other related information?

5 Related Questions:

1. How do you calculate the earliest start (ES) and latest start (LS) times in a project network?
2. What is slack time, and how can it be calculated in CPM?
3. How does the critical path impact overall project management?
4. Can there be more than two critical paths in a complex project?
5. How do dependencies between tasks affect the determination of the critical path?

Tip: Always verify if all task dependencies and durations are accurately reflected before performing critical path analysis.