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Based on the image you uploaded, I see the Project Management problem set related to determining the critical path, which involves calculating the longest path in a project network. You are provided with details about each task, including:

1. The predecessors of each task
2. Normal and crash times
3. Normal and crash costs for each activity

### (a) Draw the Critical Path Diagram
The diagram appears to be already drawn on your worksheet with nodes representing each activity (A, B, C, D, E, F, G) and directed edges representing the task sequences with their durations labeled.

To confirm the critical path, we can:
1. Calculate the earliest start and finish times for each activity.
2. Identify the path with the longest duration, which constitutes the critical path.

Based on the information provided, the following paths should be examined:

1. \( A \rightarrow B \rightarrow E \rightarrow G \)
2. \( A \rightarrow C \rightarrow F \rightarrow G \)
3. \( A \rightarrow D \rightarrow E \rightarrow G \)

After calculating the total time for each path, the path with the maximum time will be the critical path. 

Would you like me to calculate the total time for each of these paths to identify the critical path and analyze further? 

### Further Questions:
1. Do you want to know the specific steps to find the earliest and latest start/finish times?
2. Are you interested in seeing how crashing affects the critical path?
3. Would you like a breakdown of cost impacts when crashing specific activities?
4. Would you like assistance with determining which activities to crash to minimize project duration?
5. Are you interested in any alternative methods to calculate the critical path?

**Tip:** For project management tasks, always identify activities that can't be delayed without affecting the overall project duration; these are critical path activities.

After receiving an A in Operations Management, you have been hired for a summer job in Beijing as a Project Manager. The activities, their predecessors, and respective time estimates are provided. The tasks include determining the critical path and analyzing crash costs.

This problem involves determining the critical path for a project with given activities, predecessors, and time estimates. Key concepts include calculating earliest and latest start times, crash costs, and analyzing paths for project optimization. Ideal for students studying project management and operations.

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