2. (25 points) Hyper Star is a retail store that has a checkout counter with six cashiers and a self- checkout counter with two machines. Shoppers form a single line to go to one of the six cashiers, and another single line to use the two self-checkout machines. A study of the checkout process has shown that, on average, 120 customers per hour need to check out their items, some of whom use the self-checkout. The study also provided the following information: (i) the average time a cashier spends with a shopper to scan, receive payment, and bag her items is about 3 minutes, and on average, there are about one of the six cashiers idle, (ii) the are an average of 10 shoppers waiting in the line to go to cashiers, (iii) self-checkout also has an average of one machine idle, (iv) the average time from when a shopper joins the line for self-checkout until she bags her items and leaves the self-checkout counter is about 5 minutes. (a) Draw the process-ow chart of checkout at Hyper Star. (b) How much should a shopper who does not use the self-checkout machine expect to wait in the cashier's line until he/ she gets to one of the cashiers? (c) What fraction of customers is using the self-checkout counter? (d) What is the average time that a shopper uses a self-checkout machine