Please answer:

Office Equipment, Inc. [DEI] leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer's business site within an average of 3 hours from the time that the customer notifies DEI of an equipment problem. Currently, DEI has 1|] customers with service contracts. Doe service technician is responsible for handling all service calls. A. statistical analysis of historical service records hdicates that a customer requests a service call at an average rate of one call per 5|] hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer's office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for senrice, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, after the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel the to reach the new customer's ofce and an average of 1.5 hours to complete the repair senrice. The cost of the service technician is Still per hour. The downtime cost {wait time and service time] for customers is $100 per hour. {JEI is planning to expand its business. Within 1 year, OEI projects that it will have 211 customers, and within 2 years, DEI projects that it will have so customers. Although OEI is satisfied that one service technician can handle the 1:) existing customers, management is concerned about the ability of one technician to meet the average 3-hour service call guarantee when the OEI customer base expands. In a recent planning meethg, the marketing manager made a proposal to add a second service technician when DEI reaches 20 customers and to add a third service technician when UEI reaches 30 customers. Before making a final decision, management would like an analysis of (El service capabilities. DEI is particularly interested in meeting the average 3-hour waiting time gsarantee at the lowest possible total cost. Managerial Report Develop a managerial report [1 ,lJIJll-i ,25-(1 words] smimarizing your analysis of the {JEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 2|] and then Iii] customers, and justify your respmse. Include a discussion of the following issues in your report: 1. What is the arrival rate for each customer? 2. What is the service rate in terms of the number of customers per hour? {Remember that the average travel time of 1 hour is counted as service time because the time that the service technician is busy handling a service call includes the travel time in addition to the time required to complete the repair.] 3. Waiting line models generally alume that the arriving customers are in the same location as the service facility. Consider how DEI is different in this regard, given that a service technician travels an average of 1 hour to reach each customer. How should the travel time and the waiting time predicted by the waiting line model be combined to determine the total customer waiting time? Explain. 4. (El is satisfied that one service technician can handle the 11] existing customers. Use a waiting line model to detemthe the following information: {a} probability that no customers are in the system, [bi average nurrber of customers in the waiting line, {c} average number of customers in the system, {d} average time a customer waits until the service technician arrives, [e] average time a customer waits until the machine is back in operation, [f] probability that a customer will have to wait more than one hour for the service tecl'nician to arrive, and {g} the total cost per hour for the service operation. 5. Do you agree with (El management that one technician can meet the average 3-hour service call guarantee? Why or why not? 6. What is your recommendation for the number of service technicians to hire when DEI expands to 2:] customers? Use the information that you developed in (arestion 4 [above] to justify your answer. ?. What is your recommendation for the number of service technicians to hire when DEI expands to 30 customers? Use the information that you developed in (arestion 4 [above] to justify your answer. 8. What are the annual savings of your recommendation in Qtestion a {above} compared to the planning committee's proposal that 30 customers will require three service technicians? [Assume 150 days of operation per year.) How was this determination reached