https://file.aiquickdraw.com/mathbot/file/1724323955170zfn6nw1l.jpg

The graph above shows the optimal production schedule for parts \( P_2 \), \( P_3 \), and \( P_1 \) based on the total production times. The cumulative production times are:

- **\( P_2 \)**: 10,845 minutes
- **\( P_3 \)**: 15,045 minutes
- **\( P_1 \)**: 19,245 minutes

The parts are produced sequentially, with \( P_2 \) being produced first, followed by \( P_3 \), and finally \( P_1 \). This sequence minimizes the total production time.

Would you like more details or have any questions about the solution?

Here are 5 related questions to expand your understanding:
1. How would the production schedule change if the setup time was different for each part?
2. What if the parts had different priorities? How would that affect the schedule?
3. How can we reduce the total production time further?
4. What would happen if there were constraints on machine availability?
5. How does the scheduling problem change with more parts or more machines?

**Tip:** In real-world manufacturing, reducing setup time can significantly improve production efficiency, often more than optimizing run times alone.

Explore the optimal production schedule for parts P2, P3, and P1 based on total production times. This solution details the sequential production strategy minimizing production time. Learn about setup time, production efficiency, and machine availability.

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