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$\%$u$2019$s business site within an average of three hours from the time that the customers notifies OEI of an equipment problem. Currently, OEI has $20$ 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. If the service technician is available when a customer calls for service, it takes the technician an average of $1$ hour travel time to reach the customer$\%$u$2019$s office and an average of $1\mathrm{.}5$ 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 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 commitment, the technician takes an average of $1$ hour travel time to reach the new customer$\%$u$2019$s office and an average of $1\mathrm{.}5$ 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. $-$Probability that no customers are in the system $-$ Average number of customers in the waiting line $-$ Average number of customer in the system $-$ Average time a customer waits until the service technician arrives $-$ Average time a customer waits until the machine is back in operation $-$ Probability that a customer will have to wait more than one hour for the service technician to arrive $-$ The number of hours a week the technician is not making service calls $-$ The total cost per hour for the service operation Do you agree with the OEI management that one technician can meet the average three$-$hour service call guarantee? Explain