UTea is a tea shop that is famous for its signature cream cheese topped bubble tea. Inexplicably, when the shop first opened, the demand for this drink was very high with customers arriving every 45 seconds to the St. George campus shop during the day. At the shop three baristas serve the customers, taking on average two minutes for each customer. Because of different skill levels and the complicated process of making the drinks, the overall variability of the service process is CVp = 0.9. Assume arrivals are random (CV a =1). a) [5pts] What was the average wait time for customers in line at UTea in minutes? b) [5 pts] After the shop was open for a few weeks, UTea noticed that the number of customers joining the line decreased. In fact, it appeared that the average line length was 3 customers. What is the new demand rate in customers per hour? What is the percentage decrease in sales (i.e., throughput)? c) [5 pts] To improve its profitability, UTea developed a mobile app so that customers can order from their phones and then pick up their orders in store. Upon launch, UTea found on average 40 orders per hour coming from the app. It also appeared that the online (mobile)customers did not care about the wait time. UTea serves the online and offline (in-store) orders in a first come/first served order using the next available barista. Assume the processing time does not change for the online orders and CVa =1 for the mobile orders. Offline (i.e., in-store) customers still arrived so there were average of three visible customers in line. How many off-line customers are served per hour now? What is the total number of customers per hour? d) [5 pts] Based on our discussion of the Paramount Diner case, what do you expect will happen next at UTea regarding the demand mix between online and offline? What are the implications for UTea? (1-2 paragraphs)