In a bank there are two bank tellers behind the window. The demand rate is 43 customers per hour. The bank’s utilization is 90%.

Round your answer to 3 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers.

The bank’s flow rate is
customers per hour.

The total capacity of the two bank tellers is
customers per hour.

The capacity of one bank teller is
customers per hour.

The processing time per customer per bank teller is
minutes.

Let's analyze the problem step-by-step:

1. **Flow Rate:**  
   The flow rate represents the rate at which customers are served by the bank. It is given as 43 customers per hour. Thus, the flow rate is:

   \[
   \text{Flow Rate} = 43 \text{ customers/hour}
   \]

2. **Utilization:**  
   The bank's utilization is given as 90%, which means the system is operating at 90% of its full capacity. If the bank’s utilization is given as:

   \[
   \text{Utilization} = 0.90
   \]

   The flow rate is related to the total capacity and utilization by the formula:

   \[
   \text{Flow Rate} = \text{Total Capacity} \times \text{Utilization}
   \]

   Solving for total capacity:

   \[
   \text{Total Capacity} = \frac{\text{Flow Rate}}{\text{Utilization}}
   \]
   Substituting the values:

   \[
   \text{Total Capacity} = \frac{43}{0.90} = 47.778 \text{ customers/hour}
   \]

3. **Capacity of One Bank Teller:**  
   Since there are two bank tellers, we can divide the total capacity by 2 to get the capacity of each teller:

   \[
   \text{Capacity of One Bank Teller} = \frac{\text{Total Capacity}}{2} = \frac{47.778}{2} = 23.889 \text{ customers/hour}
   \]

4. **Processing Time Per Customer Per Bank Teller:**  
   The processing time is the time taken by one teller to serve one customer. The formula for processing time per customer is:

   \[
   \text{Processing Time} = \frac{60}{\text{Capacity of One Bank Teller}} \text{ minutes}
   \]
   Substituting the value of the capacity of one teller:

   \[
   \text{Processing Time} = \frac{60}{23.889} = 2.512 \text{ minutes/customer}
   \]

### Final Answers:
1. **The bank’s flow rate:** 43 customers per hour  
2. **The total capacity of the two bank tellers:** 47.778 customers per hour  
3. **The capacity of one bank teller:** 23.889 customers per hour  
4. **The processing time per customer per bank teller:** 2.512 minutes

Do you want more details on any of these calculations? Here are some related questions:

1. What would happen to the processing time if there was only one teller?
2. How would the utilization change if the flow rate increased to 50 customers per hour?
3. What is the maximum number of customers that can be served per hour with the current capacity?
4. How would the bank's efficiency be affected by reducing the number of tellers?
5. What is the idle time of each teller when utilization is less than 100%?

**Tip:** Utilization helps to understand how efficiently the system is working, but operating at 100% utilization can lead to long wait times for customers.

In a bank there are two bank tellers behind the window. The demand rate is 43 customers per hour. The bank’s utilization is 90%. Round your answer to 3 digits after the decimal point if it is not an integer. Do NOT use comma in your numeric answers. The bank’s flow rate is customers per hour. The total capacity of the two bank tellers is customers per hour. The capacity of one bank teller is customers per hour. The processing time per customer per bank teller is minutes.

This problem calculates the flow rate, total capacity, and processing time for bank tellers based on a demand rate of 43 customers per hour and a 90% utilization rate. It explores key concepts like flow rate, utilization, and processing time, and is suitable for Grades 11-12 students.

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