(8 points) Call Center Your firm's management team has decided to make customer service a high priority. This includes providing fast response time in their call center where most of the interactions with customers are happening. You have been charged with analyzing the current performance of the call center and assist them in scheduling staff that will achieve certain response time goals. Data collection for the past few months reveal that call durations are about 14 minutes with enough variabilit to make the exponential distribution a decent fit for the duration of calls. Furthermore, the demand on the call center staff varies greatly during the course of the day. The mean number of arrivals is listed in the table below for two-hour time windows during the center's working hours from 7 am to 9pm. For each time period, assume that the number of calls arrive according to a Poisson Process with the rate as stated in the table above. (a) (1 points) Select an appropriate queueing model that allows you to make staffing recommendations and answer the questions in part (c). Identify a proper model and specify all parameters. (b) (3 points) For each time period, determine (b1) a lower bound on the number of staff needed so that the system is stable, i.e., so that utilization stays below one; (b2) how many consultants the firm would need for each 2 hour interval in order to achieve their desired service standard of an expected customer wait time (time on hold) of less than four minutes? (b3) the utilization based on your recommended staffing level. (c) (2 points) Some assumptions underlying the model you are using in part (b) may not be satisfied. List two to three of those assumptions and explain why they may not hold here. (d) (2 points) What staffing schedule would you recommend? Note that employees will only work for a contiguous 4 hour shift; this may necessitate balancing the cost of hiring more staff or allowing longer wait times than the given threshold. Explain how you proceed in your scheduling decisions