b) (5 points) During the morning rush hours, an average of 100 customers per hour arrives at the coffee shop. What is the utilization of the cashier? How about the frozen drink maker and the espresso drink maker? c) (5 points) If all breakfast pastries are sold at half price, the manager expects that 50% of all customers will order food, and the overall arrival rate of customers will not change. In this case, how many customers is the coffee shop able to serve per hour? d) (5 points) Without hiring any additional employees, will the manager be able to cross- train the employees and guarantee that all customers' demand can be met even when breakfast pastries are priced at 50% off (yes/no)? What is your recommendation, and why? Question 1. (20 points) The manager of the coffee shop on campus is considering a promotion on all breakfast pastries (half price!), which marketing surveys predict will lead to a significant increase in the percentage of customers ordering food. Before launching this campaign, however, the manager would like to make sure that her coffee shop is able to meet this increase in demand. She gathered the following data. I. There are three employees working at the coffee shop: The cashier takes all orders, prepares nonbeverage food items, grinds coffee, and pours drip coffee. The frozen drink maker who prepares blended and iced drinks. The espresso drink maker prepares espressos, lattes, and steamed drinks. II. There are typically four types of customers: Drip coffee customers order only drip coffee. This requires 20 seconds of the cashier's time. On average, 25% of all customers are drip coffee customers. Blended and iced drink customers order a drink that requires the use of the blender. These drinks take on average 2.5 minutes of work of the frozen drink maker. Overall, 20% of all customers will order a blended or iced drink. Espresso drink customers order a beverage that uses espresso and/or steamed milk. On average, these drinks require 1 minute of work of the espresso drink maker. Espresso drinks are the most popular - a half of all customers are espresso drink customers. 5% of all customers come to the coffee shop to buy one of the store's many varieties of whole bean coffee and have it ground to their specification at the store. The grounding takes a total of 1 minute of the cashier's time. III. Each customer spends, on average, 20 seconds with the cashier to order and pay. IV. Approximately 25 percent of all customers order food, which requires an additional 20 seconds of the cashier's time per transaction. a) (5 points) Which one of the three employees is the bottleneck?