https://file.aiquickdraw.com/mathbot/file/1729109486530802tunlw.jpg

The project scheduling problem depicted in the image uses two processors and a priority list of tasks. The goal is to assign the tasks to the processors while respecting the precedence constraints shown by arrows and using the priority list provided.

The priority list provided is:  
**T4, T5, T7, T1, T6, T2, T3**

### Precedence Constraints
- Task T1 (4) and T2 (11) must be completed before T4 (12).
- Task T3 (7) must be completed before T5 (5).
- Task T4 (12) and T5 (5) must be completed before T6 (6).
- Task T6 (6) and T7 (10) must be completed before reaching the "End".

### Steps for Scheduling with Two Processors

1. Start by assigning tasks from the priority list that are available (i.e., those that have no unmet dependencies).
2. Keep track of which tasks each processor is working on, making sure to respect the precedence constraints.
3. Continue assigning tasks from the priority list until all tasks are completed, ignoring idle time.

### Let's solve this:

**Step 1:**
- The first available tasks according to the priority list are T1 (4), T2 (11), and T3 (7).
- Processor 1 takes T1 (4).
- Processor 2 takes T2 (11).

**Step 2:**
- When Processor 1 finishes T1, Processor 1 can now work on T4 (12), which depends on T1.
- Processor 2 is still working on T2.

**Step 3:**
- Once T2 is done, Processor 2 works on T5 (5), which depends on T3. T3 hasn’t started yet, so Processor 1 takes T3 (7).

**Step 4:**
- When Processor 1 finishes T3, Processor 2 can start T5.
- Processor 1 can continue to T4 (12) after finishing T3.

**Step 5:**
- Processor 1 finishes T4 and starts T6 (6), which depends on T4.
- Processor 2 finishes T5 and takes T7 (10), which depends on T5.

**Step 6:**
- Processor 1 finishes T6 and is idle, waiting for Processor 2 to finish T7.
- Once both are done, the project is complete.

### Processor Scheduling Output:
- **Processor 1:** T1, T4, T3, T6
- **Processor 2:** T2, T5, T7

Let me know if you'd like more details or clarifications!

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Here are 5 follow-up questions based on the information:
1. What are the precedence constraints for T4 and T5?
2. How would the project change if there were three processors instead of two?
3. What would happen if we altered the priority list?
4. Can any task be executed simultaneously by both processors?
5. How would introducing a third dependency to T6 impact the schedule?

**Tip:** When scheduling, always look ahead to see which tasks will become available as soon as predecessors are completed to minimize idle time.

Using the priority list T4, T5, T7, T1, T6, T2, T3, schedule the project below with two processors.

Learn how to solve a project scheduling problem using two processors with the task priority list T4, T5, T7, T1, T6, T2, T3. This problem involves precedence constraints, graph theory, and scheduling techniques. Suitable for college-level students.

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