Office Equipment, Inc. (OEI) 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 three hours from when the customer notifies OEI of an equipment problem. Currently, OEI has ten customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. Suppose the service technician is available when a customer calls for service. In that case, 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 service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, once the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer's office and an average of 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. The downtime cost (wait time and service time) for customers is $100 per hour. OEI is planning to expand its business. Within one year, OEI projects that it will have 20 customers, and within two years, OEI projects that it will have 30 customers. Although OEI is satisfied that one service technician can handle the ten existing customers, management is concerned about one technician's ability to meet the average three-hour service call guarantee when the OEI customer base expands. In a recent planning meeting, the marketing manager proposed adding a second service technician when OEI reaches 20 customers and adds a third service technician when OEI reaches 30 customers. Before making a final decision, management would like an analysis of OEI service capabilities. OEI is particularly interested in meeting the average three-hour waiting time guarantee at the lowest possible total cost. Develop a project report summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 customers and when OEI reaches 30 customers. Include a discussion of the following issues in your report: OEI is satisfied that one service technician can handle the ten existing customers. Use a waiting line model to determine the following information: Probability that no customers are in the system   Probability that a customer will have to wait more than one hour for the service technician to arrive Average time a customer waits until the service technician arrives