please show how to do each problem. show the formulas and explanation. I need to know how to do then to get an A on my next test.

Operations & Supply Chain Management Name: Waiting Line Review Problem: Quiz 6 (due Wednesday, April 7 at 9am) Mark A. McComb, Ph.D. Scenario: The auxiliary bookstore in the student center of a university is a small facility that sells school supplies and snacks. It has one checkout counter where one employee operates the cash register. Customers arrive at a rate of 24 per hour according to a Poisson distribution and service times are exponentially distributed with a mean of 30 customers per hour (so this a Single-server Model). The bookstore manager wants to determine the performance characteristics of this system and a few other items. Thus, she wants to know the following. Show some work to obtain credit 1. What is the utilization of the system? 2. What is the average number of customers in the system (that is, waiting and being served)? 3. What is the average number of customers in the waiting line? 4. What is the average time a customer spends in the system (that is, waiting and being served)? Show your answer in minutes. 5. What is the average time a customer spends waiting in line to be served? Show your answer in minutes. 6. On average, how many minutes each hour is the employee idle? 7. Suppose the manager sets an improvement goal to reduce the average time a customer spends in the system to 6 minutes; what service rate is required to achieve this goal? Operations & Supply Chain Management Name: Waiting Line Review Problem: Quiz 6 (due Wednesday, April 7 at 9am) Mark A. McComb, Ph.D. Scenario: The auxiliary bookstore in the student center of a university is a small facility that sells school supplies and snacks. It has one checkout counter where one employee operates the cash register. Customers arrive at a rate of 24 per hour according to a Poisson distribution and service times are exponentially distributed with a mean of 30 customers per hour (so this a Single-server Model). The bookstore manager wants to determine the performance characteristics of this system and a few other items. Thus, she wants to know the following. Show some work to obtain credit 1. What is the utilization of the system? 2. What is the average number of customers in the system (that is, waiting and being served)? 3. What is the average number of customers in the waiting line? 4. What is the average time a customer spends in the system (that is, waiting and being served)? Show your answer in minutes. 5. What is the average time a customer spends waiting in line to be served? Show your answer in minutes. 6. On average, how many minutes each hour is the employee idle? 7. Suppose the manager sets an improvement goal to reduce the average time a customer spends in the system to 6 minutes, what service rate is required to achieve this goal