EXCEL WORKSHEET

In the question below I am stuck on #3. I do not know how to find the costs associated with the customers waiting for over 4 minutes. I am able to find how many customers wait over the 4-minute threshold fine, but i am unsure on how to combine that group of people with the probability pass offs. I can calculate the probability payoffs on their own but not able to do it for only specific ones (the people over 4 minutes)

As a manager of a fast-food restaurant, you are considering opening a drive-through window. You want to start with a single window to serve cars arriving on average every 5 minutes, following a Poisson process. Your restaurant sells a variety of sandwiches, so that the time it takes to a serve a customer is variable. However, from your experience, you know that it takes on average 3 minutes to serve a customer, and the service time can be approximated by an exponentially distributed random variable. Going over your financial records you have found that, without considering the operating cost of the drive-through window, the profit from serving each customer is $5 on average. However, long waiting times for the drive-through service will create negative word-of-mouth and may result in the loss of some regular customers. Your marketing manager predicts that the restaurant will lose 25 cents per minute per car waiting in the drive-through queue. Single Server Window (20 Marks) To answer questions 1 to 3 you may create a simulation model in an Excel worksheet. Use a sample size of 2000 arrivals for your simulation. The operations manager estimates that the operating cost of the drive through window is $15 per hour, so you feel it could be profitable to open the window. However, before finalizing you decision, you decide to simulate the drive through window to make sure that it is profitable. Use Excel to build your simulation model, for answering the following questions. 1. Is there at least a 95% chance that the window is profitable? The operations manager warns you that, to avoid excessive fatigue (causing quality and safety problems), the employee who works at the drive through window should not be busy more than 85% of their shift. 2. Using your simulation model, determine if the current setting meets this criterion. Your marketing manager suggests announcing a maximum 4-minute waiting time guarantee. With this policy, if a customer waits more than 4 minutes in the line until their service starts, they will be served for free, which costs the restaurant $2 (70\% of the time) or $3 (30\% of the time). 3. Using your simulation model, estimate the average profit of the drive through window per hour under this new policy