https://file.aiquickdraw.com/mathbot/file/17295865208451lomcvxx.jpg

Based on the image provided, we have the following information related to setting up an assembly line for producing Personal Digital Assistants (PDAs):

### Task Times and Predecessors
The tasks, times, and immediate predecessors are:
- **Task A**: 12 seconds, no predecessor
- **Task B**: 15 seconds, predecessor A
- **Task C**: 8 seconds, predecessor A
- **Task D**: 5 seconds, predecessors B and C
- **Task E**: 20 seconds, predecessor D

### Goals
- The production goal is to produce **180 PDAs per hour**.

### Part (a) - Cycle Time
The cycle time is calculated by dividing the available time per hour by the required output per hour. Since there are **3600 seconds in an hour**, and the goal is to produce **180 PDAs**, we calculate:

\[
\text{Cycle Time} = \frac{3600 \text{ seconds}}{180 \text{ PDAs}} = 20 \text{ seconds per PDA}
\]

This confirms the value of **20 seconds** for cycle time.

### Part (b) - Theoretical Minimum Number of Workstations
Theoretical minimum number of workstations is determined by the formula:

\[
\text{Theoretical Minimum} = \frac{\text{Total Task Time}}{\text{Cycle Time}}
\]

The total task time is:
\[
12 \text{ (Task A)} + 15 \text{ (Task B)} + 8 \text{ (Task C)} + 5 \text{ (Task D)} + 20 \text{ (Task E)} = 60 \text{ seconds}
\]

Now, applying the formula:

\[
\text{Theoretical Minimum} = \frac{60 \text{ seconds}}{20 \text{ seconds per PDA}} = 3 \text{ workstations}
\]

This matches the value of **3 workstations**.

### Part (c) - Activity Assignment
The next part involves assigning tasks to workstations. It is based on balancing the workload across workstations, while respecting task precedence. Here is the suggested assignment:

- **Workstation 1**: Task A
- **Workstation 2**: Task B and Task C
- **Workstation 3**: Task D and Task E

This assignment ensures that each workstation does not exceed the cycle time of 20 seconds and follows the precedence relationships between tasks.

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Would you like more details on any of these steps or calculations?

### Follow-up Questions:
1. How is the cycle time influenced by increasing or decreasing the production target?
2. What happens to the theoretical minimum number of workstations if one of the task times increases significantly?
3. Can we still balance the workload if the task times change?
4. How could we adjust the workstation assignments if a fourth workstation were added?
5. What are some strategies to reduce the total task time in assembly lines?

### Tip:
When calculating the theoretical minimum number of workstations, always round up to ensure that no workstation exceeds the cycle time limit.

Amelio Rodriguez Computing wants to establish an assembly line for producing a new product, the Personal Digital Assistant (PDA). The tasks, task times, and immediate predecessors for the tasks are as follows: Task A (12 seconds, no predecessor), Task B (15 seconds, predecessor A), Task C (8 seconds, predecessor A), Task D (5 seconds, predecessors B and C), Task E (20 seconds, predecessor D). Amelio's goal is to produce 180 PDAs per hour.

Learn how to calculate cycle time and assign tasks to workstations for the production of Personal Digital Assistants (PDAs). This problem involves calculating the cycle time for a production rate of 180 PDAs per hour, determining the theoretical minimum number of workstations, and assigning tasks while respecting task precedence. Suitable for college-level operations management or industrial engineering students.

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