In a pull system, the utilization of a machine is determined by the demand rate, and since the demand for apples exceeds supply, the pull system would operate based on the capacity of the machine with the lowest throughput.

Here, the capacities are:

• Cleaning machine capacity = 1,500 apples per hour
• Labeling machine capacity = 500 apples per hour

In a pull system, the bottleneck will be the labeling machine, because it has the lowest capacity (500 apples per hour).

To find the utilization of the cleaning machine, we need to determine how much of its capacity is being used, which is driven by the labeling machine's capacity (since the cleaning machine has a higher capacity but will be synchronized to match the labeling machine's throughput).

Utilization Formula:

$\text{Utilization of cleaning machine} = \frac{\text{Demand rate}}{\text{Capacity of cleaning machine}} = \frac{\text{Capacity of labeling machine}}{\text{Capacity of cleaning machine}}$

Now, substitute the given values: $\text{Utilization of cleaning machine} = \frac{500}{1500} = 0.333$

Thus, the utilization of the cleaning machine is 0.333, or 33.3% when rounded to three decimal places.

Let me know if you have any further questions or need clarification!

Further questions to explore:

1. What is the utilization of the labeling machine in this system?
2. How would the system be affected if the labeling machine capacity increased to 1,000 apples per hour?
3. What would happen to the system's overall throughput if the cleaning machine capacity decreased to 1,200 apples per hour?
4. How does the concept of a bottleneck apply in manufacturing systems, and why is it important?
5. What is the relationship between machine utilization and system efficiency in a pull system?

Tip: Always identify the bottleneck in a pull system, as it dictates the pace of the entire process.