Question 1. (Total 50 points) A new student-run caf has just opened on campus, offering their own, locally brewed specialty coffees. The first week of operations was more popular than anticipated and there were long line ups at the caf; it was observed that on average 40 customers per hour arrived at the caf; on average, it took 6.75 minutes to serve a customer. During the hours of operation, there were 5 employees serving the counter. Based on the first week of operations, determine the following: a) On average, how many customers were at the counter (including those being served)? b) What was the average time a customer had to wait to be served in minutes)? c) If a customer had to wait, how long was the average wait time in minutes)? d) What is the probability a customer will have to wait for service? As a result of the first week, the students are considering increasing the number of employees serving the counter. To help to make the decision, they have learned from their marketing professor that industry standards suggest a waiting customer costs a company $7.50/hour; they have also determined that each additional employee will actually increase service time by half a minute. Employees are paid $15/hour. e) Determine the total hourly cost at the current level (5 employees) and with additional employees. How many employees minimize total cost? f) Recalculate the performance measures of a), b), c) and d) with the number of employees recommended in part e). What do you notice about the new performance measures