Using this information, answer part c$)$: $($a$)$ You ask Mark to describe the demand and service rate. He tells you that calls are randomly received by the call center and that the center receives an average of $70$ calls per hour. The computer system installed to answer and hold the calls is so advanced that its capacity far exceeds the demand. Because the nature of a call is random, the time required to process a call is random, where the time frequently is small but occasionally can be much longer. On average, however, representatives can handle $6$ calls per hour. Which queueing model seems appropriate for this situation? Given that slightly more than $35$ percent of customers wait over $4$ minutes before a representative answers the call, use this model to estimate how many representatives Mark currently employs. $($b$)$ Mark tells you that he will not be satisfied unless $95$ percent of the customers wait only $1$ minute or less for a representative to answer the call. Given this customer service level and the average arrival rates and service rates from part $($a$),$ how many representatives should Mark employ? $($c$)$ Each representative receives an annual salary of $$30,000,$ and Mark tells you that he simply does not have the resources available to hire the number of representatives required to achieve the customer service level desired in part $($b$).$ He asks you to perform sensitivity analysis. How many representatives would he need to employ to ensure that $80$ percent of customers wait $1$ minute or less? How many would he need to employ to ensure that $95$ percent of customers wait $90$ seconds or less? How would you recommend Mark choose a customer service level? Would the decision criteria be different if Mark's call center were to serve external customers $($not connected to the company$)$ instead of internal customers $($employees$)$