Problem 1:

Consider a 24-hour call center which provides tech support for a software company. There are currently 85 operators who can answer calls at any moment in time. It takes, on average, 10 minutes for an operator to solve a customers problem, with a coefficient of variation of 2. Assume that the number of calls per hour does not vary much throughout the day, and averages 500 calls an hour. The standard deviation of the time between two calls is equal to 6 seconds. If a customer calls when all operators are busy answering calls, he or she is put on hold. Customers on hold are then answered on a first-come-first-served basis. Assume that there is no limit to the number of customers who can be on hold at any moment in time and that callers do not get impatient and always stay on hold until they speak to an operator.

1. How long does a customer spend waiting on hold, on average?
2. What is the average number of customers that are on the phone with the call center (either on hold or talking to an operator) at any point in time?
3. What is the average number of calls completed by one operator in one hour?
4. What is the average number of operators who are not on the phone with a customer at a given moment in time?
5. What percentage of the time spent on the phone by a customer is spent on hold?
6. Suppose now that the call center only has a certain number of phone lines. If all the lines are used (by customers who are either talking to an operator or waiting on hold), then the next customer gets a busy signal. What is the minimum number of phone lines that are necessary so that no customer ever gets a busy signal?
7. Suppose that, instead of answering calls on a first-come-first-served basis, the call center decides to give priority to first-time callers (whom they can identify from their phone number). Would this new policy change your answer to (a)? Just say yes or no then explain why or why not. Hint: there is not really a correct answer as to yes or no. It all depends on your justification.
8. (Disregard (g)) The call center estimates that it costs them $1 per minute that a customer spends waiting on hold. Operators are paid $20 per hour. The call center manager is considering hiring 5 more operators. Is it wise?

Any help is much appreciated