Suppose you are the manager of a coffee shop with three servers, who each take an average of 1.6 minutes to serve a customer. You are concerned about your service during peak hours, and are considering making an investment to improve service.

During peak hours, you have 1.2 customers per minute arriving on average. You have two options to ensure faster service: (a) hire a fourth server at an annual cost of $43,000, or (b) rent faster dispensing machines at an annual cost of $33,000, which would reduce service time to 1.25 minutes, on average. You would like to find the cheapest solution that will allow you to serve the customers adequately - and you decide this means that you don't want to have a more than 10% chance of more customers arriving than you can serve. For instance, with your current operation, you can serve three customers in 1.6 minutes, so you don't want the chance of more than three customers within 1.6 minutes to be greater than 10%.

What should you do - continue the current operation, hire a fourth server, or rent faster dispensing machines? (HINT: For each scenario, calculate the probability that customers arrive in numbers larger than the number that can be served at the same time to verify if it is less than 10%. Make sure to adjust your Lamda parameter to the proper unit of time in each scenario; for example, for the current operation, the arrival rate per time to serve 3 customers is 1.6*1.2=1.92.)

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