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To solve this problem, we need to reduce the total project duration from 9 weeks to 6 weeks by "crashing" certain activities. Crashing an activity means reducing its duration at a cost. Here's the process we'll follow:

### Project Activities and Durations:
- **A (Start)**: 2 weeks
- **B**: 2 weeks
- **C**: 5 weeks
- **E**: 1 week
- **F (End)**: 2 weeks

### Crash Cost Per Week:
- **A**: $380 per week
- **B**: $120 per week
- **C**: $200 per week
- **E**: $150 per week
- **F**: $420 per week

### Precedence:
- **A** precedes **B** and **C**.
- **B** and **C** precede **E**.
- **E** precedes **F**.

### Steps to Solve:
1. **Total Duration**: The longest path, also called the critical path, dictates the project's completion time.
    - Path 1: A → B → E → F (2 + 2 + 1 + 2 = 7 weeks)
    - Path 2: A → C → E → F (2 + 5 + 1 + 2 = 10 weeks)

   Therefore, **Path 2 (A → C → E → F)** is the critical path, as it takes 10 weeks. We need to reduce this path to 6 weeks.

2. **Weeks to Reduce**: We need to crash activities on Path 2 by **4 weeks** (from 10 to 6 weeks).

3. **Crash Activities with Minimum Cost**: To reduce the duration cost-effectively, we crash the activities with the lowest crash cost first.

Let's proceed step by step to calculate the required reductions.It seems like I can’t do more advanced data analysis right now. Please try again later. Would you like me to manually walk you through the process of solving this problem, or would you prefer to attempt the calculation yourself?

Here are 5 related questions for further understanding:
1. What is a critical path in project management?
2. How does crashing an activity help reduce project duration?
3. What are the trade-offs of reducing project duration through crashing?
4. How does the precedence of activities affect which activities can be crashed?
5. How would the project cost change with different crash durations?

**Tip:** Always prioritize crashing the activities with the lowest cost on the critical path to optimize the project duration.

The following is a table of activities associated with a project at Rafay Ishfaq's software firm in Chicago, their durations, what activities each must precede, and the crash cost to reduce duration per week: 

Suppose that Rafay is only given 6 weeks (instead of 9) to complete the project. By how many weeks should each activity be crashed in order to meet the deadline?

This problem explores project scheduling optimization through crashing activities to reduce total duration from 9 weeks to 6 weeks. Using the Critical Path Method, learn to minimize costs by focusing on the most cost-effective activity reductions.

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