We will solve this problem step by step, starting with the current process flow rate and then determining how adding a server will impact the flow rate.

Step 1: Identify the processing times for each step

• Step 1 (Registration with receptionist):
  There is 1 receptionist, and each customer takes 2 minutes. $\text{Capacity of receptionist} = \frac{60 \, \text{minutes}}{2 \, \text{minutes per customer}} = 30 \, \text{customers per hour}.$

• Step 2 (Payment with cashier):
  There are 2 cashiers, and each customer takes 8 minutes. $\text{Capacity per cashier} = \frac{60 \, \text{minutes}}{8 \, \text{minutes per customer}} = 7.5 \, \text{customers per hour}.$ Since there are 2 cashiers, the total capacity is: $\text{Total capacity of cashiers} = 7.5 \times 2 = 15 \, \text{customers per hour}.$

• Step 3 (License processing stations):
  There are 3 license processing stations, and each customer takes 15 minutes. $\text{Capacity per station} = \frac{60 \, \text{minutes}}{15 \, \text{minutes per customer}} = 4 \, \text{customers per hour}.$ Since there are 3 processing stations, the total capacity is: $\text{Total capacity of license stations} = 4 \times 3 = 12 \, \text{customers per hour}.$

Step 2: Determine the bottleneck

The flow rate is determined by the slowest part of the process, i.e., the bottleneck. The capacities of each stage are:

• Receptionist: 30 customers per hour
• Cashiers: 15 customers per hour
• License stations: 12 customers per hour

The bottleneck is the license processing stations, with a capacity of 12 customers per hour.

Step 3: Calculate the flow rate with current capacity

Since the bottleneck limits the flow rate, the current flow rate of the process is: $\text{Flow rate} = 12 \, \text{customers per hour}.$

Step 4: Calculate the flow rate after adding one server to the bottleneck

By adding one more license processing station, there will be 4 processing stations in total. The capacity of the license processing stations will then be: $\text{New capacity of license stations} = 4 \times 4 = 16 \, \text{customers per hour}.$

Now, the bottleneck shifts to the cashiers, whose capacity is still 15 customers per hour. Therefore, the new flow rate will be determined by the cashiers: $\text{New flow rate} = 15 \, \text{customers per hour}.$

Final Answers:

1. Current flow rate: 12 customers per hour.
2. Flow rate after adding one server: 15 customers per hour.

Would you like further details or explanations?

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Here are 5 related questions:

1. What would the flow rate be if an additional cashier were added instead of a license station?
2. How does the concept of a bottleneck affect overall process efficiency?
3. If the cashier processing time were reduced to 6 minutes per customer, what would the new flow rate be?
4. What would happen to the flow rate if both the receptionist and the license stations had additional servers?
5. How does variability in service times impact the overall flow rate in such a system?

Tip: Always focus on the bottleneck when trying to increase the overall flow rate, as improving non-bottleneck areas may not significantly impact the total output.