Regional Airlines is revamping its telephone system for handling changes to existing flight reservations. During the $10$:$00$ a$.$m$.$ to $11$:$00$ a$.$m$.$ time period, calls to the reservation agent occur randomly at an average of one call every $3\mathrm{.}75$ minutes. Historical service time data show that a reservation agent spends an average of $3$ minutes with each customer modify$-$ing their flight reservations. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the reservation modification system.Regional Airlines$$ management believes that offering an efficient way for its custom$-$ers to modify their existing reservations is an important part of establishing an image as a service$-$oriented airline. If the system is properly managed, Regional Airlines will establish good customer relations, which in the long run will increase business. However, if the reservation modification system is frequently overloaded and customers have difficulty contacting an agent, a negative customer reaction may lead to an eventual loss of business. The cost of a reservation agent is $$20$ per hour. Thus, management wants to provide good service, but it does not want to incur the cost of overstaffing the telephone reservation modification operation by using more agents than necessary.At a planning meeting, Regional$$s management team agreed that an acceptable cus$-$tomer service goal is to answer at least $85\%$ of the incoming calls immediately. During the planning meeting, Regional$$s 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$$s conclusion was that personnel costs could be minim$-$ized by using one agent and that the single agent should be able to handle the reservation modifications and still have some idle time. The vice president of marketing restated the importance of customer service and expressed support for at least two reservation agents.To enhance its reservation modification system, if all agents are busy when a customer calls, the customer will be prompted to enter information such as their frequent flier number, reservation number, and reason for modifying the reservation. If a known flight disruption is creating the need for the modification, Regional$$s reservation software will list potential itinerary changes while the customer waits so that the reservation modification can be made quickly once an agent is available. LO $2,3$Managerial ReportPrepare a managerial report for Regional Airlines analyzing the telephone reservation modification system. Include the following information in your report:$1.$A detailed analysis of the operating characteristics of the reservation modification system with one agent as proposed by the vice president of administration. What is your recommendation concerning a single$-$agent system?$2.$A detailed analysis of the operating characteristics of the reservation modification system based on your recommendation regarding the number of agents Regional should use$\mathrm{.}3.$This report represents a pilot study of the reservation modification system for the $10$:$00$ a$.$m$.$ to $11$:$00$ a$.$m$.$ time period during which an average of one call arrives every $3\mathrm{.}75$ minutes; however, the arrival rate of incoming calls is expected to change from hour to hour. Describe how your waiting line analysis could be used to develop a plan that would enable the company to provide different levels of staffing for the reserva$-$tion modification system at different times during the day. Indicate the information that you would need to develop this staffing plan.