A manager of a medium-sized call center needs to determine the optimal number of operators that she should hire. The call center serves two types of clients: Business (B) and Leisure (L) customers. She has determined that B calls arrive according to a Poisson process at a rate of 18 calls per hour. On the other hand, L calls arrive according to a Poisson process at a rate of 50 calls per hour. She decides to hire highly skilled operators who can serve both type of customers and the average amount of time that they need is 9 minutes per call independent of the type (service times are exponentially distributed). The cost of hiring an H operator is $35 per hour. The manager has also estimated that the cost of keeping a B customer waiting in queue is $80 per customer per hour while the cost of keeping an L customer waiting in queue is $20 per customer per hour. The manager is considering having a single queue for both types of calls and hire only H operators that will serve both types of calls. Calls will be served on a First-Come-First-Serve basis independent of their type.
Find: 1. Minimum feasible number of operators
2. Average number of B and L customers in the queue if the call center is staffed by 12 operators
3. Total cost incurred by the call center per hour of operating if it is staffed by 12 operators
4. Nopt: the optimal number of operators that minimizes the cost incurred by the call center, and the corresponding cost, Wq, and utilization. Please show all your work. Be sure to include the formula for the wait cost computation.
Please show all your work. Be sure to include the formula for the wait cost computation.