Let's break this problem down step by step:

1. Resource Capacity of Step 2:

Resource capacity is calculated as the number of units a resource (machine) can process in one hour. The processing time for Step 2 is given as 15 minutes per unit.

To convert this to units per hour:

$\text{Capacity of Step 2} = \frac{60}{15} = 4 \text{ units per hour}$

2. Resource Capacity of Step 4:

Similarly, the processing time for Step 4 is 20 minutes per unit.

$\text{Capacity of Step 4} = \frac{60}{20} = 3 \text{ units per hour}$

3. Process Capacity:

The process capacity is determined by the slowest (bottleneck) step, which has the highest processing time. Here are the processing times for each step:

• Step 1: 25 minutes per unit
• Step 2: 15 minutes per unit
• Step 3: 30 minutes per unit
• Step 4: 20 minutes per unit

The bottleneck is Step 3 with 30 minutes per unit. The capacity of Step 3 is:

$\text{Capacity of Process} = \frac{60}{30} = 2 \text{ units per hour}$

4. Cycle Time:

The cycle time is the time it takes to complete one unit in a machine-paced process, which is governed by the bottleneck. Since Step 3 is the bottleneck:

$\text{Cycle Time} = \frac{1}{\text{Process Capacity}} = \frac{1}{2} = 0.5 \text{ hours per unit}$

5. Time for First Flow Unit Through an Empty System:

For the first unit to go through an empty system, it must pass through all four steps. The time is the sum of the processing times at each step:

$\text{Time for First Unit} = 25 + 15 + 30 + 20 = 90 \text{ minutes} = \frac{90}{60} = 1.5 \text{ hours}$

6. Total Time to Complete 105 Units:

Once the system is full, units are completed at the rate of the bottleneck. The first unit takes 1.5 hours, and each subsequent unit takes the cycle time of 0.5 hours. So, to complete 105 units:

• Time for the first unit: 1.5 hours
• Time for the remaining 104 units: $104 \times 0.5 = 52$ hours

Thus, the total time to complete 105 units is:

$1.5 + 52 = 53.5 \text{ hours}$

Final Answers:

• Resource capacity of Step 2: 4 units per hour
• Resource capacity of Step 4: 3 units per hour
• Process capacity: 2 units per hour
• Cycle time: 0.5 hours
• Time for the first unit to go through the system: 1.5 hours
• Total time to complete 105 units: 53.5 hours

Would you like more details on any step? Here are five related questions to consider:

1. How would adding an additional machine to Step 3 affect the process capacity?
2. If Step 1’s processing time increased to 35 minutes per unit, what would the new bottleneck be?
3. What would happen if Step 2 could process in 10 minutes per unit?
4. How do you calculate throughput time in systems with multiple machines?
5. How would a downtime of 30 minutes affect the total time for 105 units?

Tip: Identifying the bottleneck is crucial in optimizing a machine-paced process. Focusing on improving the bottleneck step can significantly increase overall process capacity.