At a single-phase, multiple-channel service facility, customers arrive randomly. Statistical analysis of past data shows that the interarrival time has a mean of 10 minutes and is exponentially distributed. The service time per customer has a mean of 4 minutes and is exponentially distributed. The arrival buffer capacity is 4 customers. The lost customer cost due to blocking is $100 per customer. The waiting cost is $50 per customer per hour. The server cost is $15 per server per hour. The Performance.xls spreadsheet was used to generate the calculations in the table below. Arrival Service Buffer Ave. Prob. Prob. Overall Ave. Ave. Rate Time Servers Cap. Util. blocking waiting queue Ave. flow Inv. (if not length wait time blocked) # of Ave. Exp. R TR P P(block) P(wait) li Ti 1 1 0.1 4 1 4 39.75% 0.61700% 39.37% 0.2440 2.46 6.46 0.642 2 0.1 4 2 4 20.00% 0.00853% 6.66.% 0.0165 0.17 4.17 0.417 3 0.1 4 3 4 13.33% 0.00023% 0.82% 0.0013 0.01 4.01 0.401 a. Find the optimal number of servers to be employed (only 1, 2, or 3 servers is possible) to minimize the total of lost customer cost, waiting cost, and server cost. b. Find the average overall waiting time and the average total flow time through the system for the optimal case. c. If a fourth server were possible what do you think would happen to total cost in a four server system