Reference no: EM13904649

Money R’Us is an all-purpose financial institution located in Dayton’s financial district. Money R’Us has 6 departments and a supervisory staff as shown below. Customers arrive at each department at random (i.e. a Poisson process) with mean arrival rates as indicated in Figure 1. Figure 1 Customer routings Shown in Figure 1are the number of customer arriving externally at each department (in bold red) per day and the fraction of customers once processed at a department that are transferred to another department for processing . Business hours are from 9:00 AM to 3:00 PM (Eastern Time zone). Table 1 provides service time and associate costs. Mean processing time in minutes per customer Cost per (6-hour) day per department associate (server) Banking #1 20 $120 Insurance #2 30 $200 Supervisor #3 15 $500 Investments #4 45 $350 Loans #5 30 $270 Mortgages #6 60 $185 Credit cards #7 15 $120 Table 1. Department Data Assume steady-state and exponential distributions in answering the following. Part (a) Determine the minimum number of associates that must be assigned to each department in order to support the workload (i.e. steady-state). Part (b) Based upon your solution to Part (a), find: (1) The total associate costs (2) The expected time a customer is in the system (3) The expected number of customers in the system Part (c) Determine the number of associates that should be assigned to each department so that the mean customer waiting time in that department is no more than 10 minutes. Part (d) Based upon your solution to Part (c), find: (1) The total associate costs (2) The expected time a customer is in the system (3) The expected number of customers in the system