I need help with equations an explanation of how to find weighted average of queuing theory. Here are the problems, answers and equations. I just need help in figuring out how they were solved... I don't understand what info was entered into the equations to find the answers

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Question

Scenario Five: Your bank has decided to open a new drive-in widow complex at the Water Street location that is more accessible to its downtown customers. The new branch will operate three lanes and will be manned using customer service personnel that can service customers at the rate of 6 customers every twenty minutes. The plan is to keep one lane open all day (9:00 AM 5:00 PM), a second lane open for 2 hours during lunch (Noon 2:00 PM) and a third lane open for 3 hours during afternoon/evening peak times (2:00 PM 5:00 PM). Assume the arrival rates for off-peak times is 3.5 customers every fifteen minutes, the arrival rate during lunch is 7 customers every twenty minutes, and the arrival rate for peak time increases to 4 customers every ten minutes. Because this location is downtown and services a more affluent client, the bank pays its customer service personnel $30.25 per hour (including benefits) and estimates the wait time cost at $75.00 per hour.

Question 37: What is the weighted average number of customers in the system?

Question 38: What is the weighted average number of customers in the queue?

Question 39: What is the weighted average time a customer spends in the system?

Question 40: What is the weighted average time a customer spends in the queue?

Question 41: What is the total (non-weighted average) wait time customers spend in the system on a typical day?

Question 42: What is the total (non-weighted average) wait time customers spend in the queue on a typical day?

Question 43: What is the total daily service cost?

Question 44: What is the total daily cost of customers waiting in the system on a typical day?

Question 45: What is the total daily cost of customers waiting in the system plus the cost of service on a typical day?

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Equations

7. Average Number of customers in the system using weighted average calculations.

Ls = [(Ls of Channel 1 * C1hrs.) + (Ls of Channel 2 * C2hrs.]/ [C1hrs. + C2hrs.]

Ls =((Ls1 * C1hrs.) + (Ls2 * C2hrs.))/(C1 hrs. + C2 hrs.)

8. Average Number of customers in the queue using weighted average calculations.

Lq = [Lq of Channel 1 * C2hrs.) + (Lq of Channel 2 * C2hrs.)]/ [C1hrs. + C2hrs.]

Lq =((Lq1 * C1hrs.) + (Lq2 * C2hrs.))/(C1 hrs. + C2 hrs.)

9. Average Time customers spend in the system using weighted average calculations.

Ws = [(Ws of Channel 1 * C1hrs.) + (Ws of Channel 2 * C2hrs.]/ [C1hrs. + C2hrs.]

Ws =((Ws1 * C1hrs.) + (Ws2 * C2hrs.))/(C1hrs. + C2hrs.)

10. Average Time customers spend in the queue using weighted average calculations.

Wq = [(Wq of Channel 1 * C1hrs.) + (Wq of Channel 2 * C2hrs.]/ [C1hrs. + C2hrs.]

Wq =((Wq1 * C1hrs.) + (Wq2 * C2hrs.))/(C1hrs. + C2hrs.)

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Answer

Solution

Rate =6 customers every twenty minutes

Arrival rates for off-peak times is 3.5 customers every fifteen minutes,

The arrival rate during lunch is 7 customers every twenty minutes, and

The arrival rate for peak time increases to 4 customers every ten minutes

The bank pays its customer service personnel $30.25 per hour (including benefits) and estimates the wait time cost at $75.00 per hour.

Therefore:

Question 37: What is the weighted average number of customers in the system?

= 10.5 customers per 20 minutes

Question 38: What is the weighted average number of customers in the queue?

= 5customers per 20 minutes

Question 39: What is the weighted average time a customer spends in the system?

= $ 350.50

Question 40: What is the weighted average time a customer spends in the queue?

= $ 705

Question 41: What is the total (non-weighted average) wait time customers spend in the system on a typical day?

Question 42: What is the total (non-weighted average) wait time customers spend in the queue on a typical day?

= $64000

Question 43: What is the total daily service cost?

= $ 4500

Question 44: What is the total daily cost of customers waiting in the system on a typical day?

= $ 32, 600

Question 45: What is the total daily cost of customers waiting in the system plus the cost of service on a typical day?

= $39, 500

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Are these the right answers and how did they come up with these answers...?