NYUYSTERN NEW YORK UNIVERSITY . LALINARD N. STERN SCHOOL OF BUSINESS Problem 2. (40 points ) The manager of the call center of a large airline company needs to determine the optimal number operators that she should hire . The call center serves two types of clients : Business (B) and Leisure (L) customers . She has determined that the inter -arrival times of both B and L calls are both exponentially distributed . Moreover , B calls arrive at a rate of 20 calls per hour and L calls arrive at a rate of 60 calls per hour Two types of operators are available on the market : High skill (H) and Average skill (A), which differ on their ability and speed to serve both types of clients . H operators can serve both types of customers and the average amount of time that they need is 10 minutes per call independent of the type . On the other hand , A operators can serve only L calls and they need on average 15 minutes per call . Assume that all service times are exponentially distributed The cost of hiring an H operator is $28 per hour while the cost of hiring an A operators is $18 per hour . The manager has also estimated that the cost of keeping a B customer waiting in queue is $50 per customer per hour while the cost of keeping an L customer waiting in queue is $5 per customer per hour. The manager is considering two possible configurations Configuration 1: Single queue Have a single queue for both type of calls and hire only H operators that will serve both types of calls. Calls will be served on a First - Come - First -Serve base independent of their type . Configuration 2: Two separate queues Have two separate queues for each type of calls . For the B calls queue , hire H operators . For the L calls queue , hire A operators 1. If the manager chooses configuration 1, what is the optimal number of H operators that she should hire ? 2. If she chooses configuration 2, what is the optimal number of H and L operators that she should hire ? 3. Briefly analyze the two configurations , select the optimal one and explain the intuition behind the result Please show all your work . Explain carefully your approach