Question: EfficientResponse specializes in providing call center services to major electronics retailers. Recently, CheapTronics, a company which had outsourced its call center operations to EfficientResponse brought up its customers' complaints about the long wait times during late hours, which is particularly an issue for the company's "gold" customers who had enrolled in CheapTronics' reward program. EfficientResponse employs only one agent during the late night shift. The number of calls during this time period is random with an average of 30 per hour and CVa=1. Service times are random as well, with CVp=1; each call takes on average 1.5 minutes (not including the wait time).
(a) CheapTronics suggests that EfficientResponse should prioritize the "gold" customers as calls are received. If the percentage of gold customers calling at late hours is 30% of the call volume, how long would they wait on average during the late hours if EfficientResponse implements the priority rule?
(b) How many agents should be on call to reduce the average wait time to 2 minutes?