Question: (26 pts) A company must staff a toll-free phone center where customers call in with questions about products. The company is trying to determine how many operators to have available. Customers call in and are put on hold to wait for the next available operator if all operators are busy. These calls come in at a Poisson rate of 30 per hour. An operator spends on average 5 minutes answering each call and those times are exponentially distributed. Assume here that the company places a value of $15 an hour on the customers’ waiting time, and that the operators are paid $20 per hour.

1. What are lambda and mu, and which model describes this setup?
2. If the company’s goal is to have the minimum total cost per hour to operate this waiting line system, how many operators should they have? For your solution, what are the expected cost per hour of the system and the average time calls are on hold, waiting for assistance?
3. If the company’s goal is to have the average time a customer spends waiting on hold for an operator to be no more than 5 minutes, how many operators should they have? For your solution, what is the average time calls are on hold, waiting for assistance?
4. If the company’s goal is to have the probability that a customer spends more than 5 minutes waiting on hold for an operator to be no more than 5%, how many operators should they have? For your solution, what is the average time calls are on hold, waiting for assistance?

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