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.