Question: Big Bruin, Inc. plans to open a small grocery store in Juneberry, NC. They expect to have two check-out lanes, with one lane being reserved for customers paying with cash. The question they want to answer is: how many grocery carts do they need? During business hours (6 A.m.-8 P.M.), cash-paying customers are expected to arrive at 8 per hour. All other customers are expected to arrive at 9 per hour. The time between arrivals of each type can be modeled as exponentially distributed random variables. The time spent shopping is modeled as normally distributed, with mean 40 minutes and standard deviation 10 minutes. The time required to check out after shopping can be modeled as lognormally distributed, with
(a) mean 4 minutes and standard deviation 1 minute for cash-paying customers;
(b) mean 6 minutes and standard deviation 1 minute for all other customers.
We will assume that every customer uses a shopping cart and that a customer who finishes shcpping leaves the cart in the store so that it is available immediately for another customer. We will also assume that any customer who cannot obtain a cart immediately leaves the store, disgusted. The primary performance measures of interest to Big Bruin are the expected number of shopping carts in use and the expected number of customers lost per day. Recommend a number of carts for the store, remembering that carts are expensive, but so are lost customers.