A process flow map for a call center is provided below. Here's how this process works. Customers with questions about this company's products call an $800$ number. During a typical $8$hour day shift, the time between calls can be approximated by an exponential distribution with a mean of $4$ minutes. The call center has $10$ phone lines and hence can handle up to $10$ calls at once. If a call arrives and all $10$ lines are in use, then the caller gets a busy signal and has to call back later. If a call arrives and fewer than $10$ lines are in use, then the call goes directly to a customer service $($CS$)$ person, if one is available, and otherwise is put on hold. The amount of time for a CS person to handle a call, once answered, can be approximated by a normal distribution, with a mean of $10$ minutes and a standard deviation of $2$ minutes.

Note: Because there are only $10$ phone lines, the number of CS people plus the capacity of Line must be $10.$

Process Flow Map for Call Center

Question: Management wants to determine how many CS people to use during the day shift so that two things are both true: the mean number of minutes a person waits is less than $2$ minutes and the service level is at least $\mathrm{.}99.$ Consider using from one to five CS people. For each possibility, run $50$ simulations of an $8-$hour day shift and record the mean cycle time through Line. Assume that the initial number of callers on hold at the beginning of the day shift can be approximated by a normal distribution with a mean of $2$ and a standard deviation of $\mathrm{.}5($SimQuick will round to the nearest integer$).$ How many CS people would you recommend for the day shift?