Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM to 2:00 PM time period, calls to the reservation agent occur randomly at an average rate of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system.
At a planning meeting, the Regional’s management team agreed that an acceptable customer service goal is to answer at least 75% of the incoming calls immediately. During the planning meeting, Regional vice president of administration pointed out that the data show that the average service rate for an agent is faster than the average arrival rate of the telephone calls. The vice president’s conclusion was that personnel costs could be minimized by using one agent and that single agent must be able to handle the telephone reservations and still have some idle time. The vice president of marketing restated the importance of customer service and expressed support for at least two reservation agents.
We already analyzed the single-agent system’s performance according to the opinion of vice president of administration. We concluded that operating the telephone reservation service with only one ticket agent appears unacceptable because they won’t be able to meet their goal. 

Evaluate the opinion of the vice president of marketing by answering the following questions:

1. What is the service rate for the 2-agent system? Interpret the number.

2. What percentage of time both agents are idle?

3. What percentage of time a caller will be blocked if the system design does not allow callers to wait?

4. What percentage of time only one ticket agent is busy?

5. What is the average number of callers in the system?

6. What is the average time in minutes that customer spends in the system within half an hour?

7. What is the total cost if the system operates for 8 hours? The cost of a ticket reservation agent is $20 per hour. The cost of waiting caller in the system is $500 per hour (because we may lose the customer due to the waiting).
What is our expected profit if, every 8 hours, 20 customers on average purchase tickets with an average value of $350?