1. In this problem, assume Poisson arrivals and exponential service times. Customers of Plaka Record rental outlet arrive at the store to rent CDs with an arrival rate of 1.25 customers per minute. The store has only 1 counter with a service rate of 2 customers per minute. a. What is the probability that no customers are in the system? b. What is the average number of customers waiting for service? c. What is the probability that an arriving customer will have to wait for service? d. What is the probability that there are 5 customers in the system?

2. Suppose that Plaka Record rental outlet adds another counter to serve the customers simultaneously. a. The average number of customers in the waiting line b. The average number of customers in the system c. The average time a customer spends in the waiting line d. The average time a customer spends in the system

3. Plaka Record rental outlet is willing to assign a cost of P500 per hour for customer waiting time and a cost of P350 for service time per hour. Perform an economic analysis on the two models. Which of the two models would you recommend? Explain.

4. (10 Points) This pandemic, PCI Bank opens a drive-thru window for customers to complete bank transactions without getting out of their cars. Arrivals occur at random, with an arrival rate of 30 customers per hour.

a. What is the mean or expected number of customers that will arrive in a five- minute period?

b. Assume that the Poisson probability distribution can be used to describe the arrival process. Compute: i. the probability that exactly 0 will arrive during a five-minute period ii. the probability that exactly 2 will arrive during a five-minute period

c. Assume that the service times for the drive-thru window follow an exponential probability distribution with a service rate of 42 customers per hour. Use the exponential probability distribution to answer the following questions: i. What is the probability the service time is one minute or less? ii. What is the probability the service time is two minutes or less?