Solve all the following problems using appropriate management science method. At least two of the problems must be solved by using a suitable software (excel, QM, POM, etc.). Show the entire steps.

1. Crisps fast-food restaurant has a drive through window with single server. The window operator is assisted by other employees who prepare the orders. Customers arrive at the ordering station every 4.5 minutes (Poisson distribution) and the service time is 2.8 minutes.

1. Determine the average length of the waiting line and the waiting time.
2. What is the probability that no customers are in the system and the service idle.
3. What is the probability a customer will have to wait to be served? Discuss the quality of the service.

2. AquaTech Service Sdn. Bhd. has 4 stations to serve customers. Customers have to line up on a first in first out basis. The mean arrival rate is FOURTY (40) customers per hour, Poisson distributed and the mean service time per server is 4 minutes, exponentially distributed. Indicate whether the company operations are effective and efficient in terms of the following;

1. Idle time of workers at the counters (servers).
2. The percentage of time a customer can walk in and get served without waiting at all
3. Customer waiting time for service and number of customer waiting for service.
4. Average time customer spends in the total queuing system.
5. The average number of customers in the queuing system