Question

Shoppers at a Piggly Wiggly store enter the store at the rate of 48 customers per hour and spend an average of 20 minutes selecting their groceries. When it comes time to check out, shoppers have their choice of two types of checkout lines; an express line for shoppers with 15 items or fewer and a single line for shoppers regardless of how many items are in their cart. About 25% of all shoppers can (and do) choose the express line. There are on average two shoppers in the express line and six shoppers in the non-express line. Once it is their turn, it takes express checkout shoppers an average of three minutes to check out and non-express customers an average of five minutes to check out.

1) How many customers are in the Piggly Wiggly at any given time?

Answer 1

To determine the number of customers at Piggly Wiggly at any given time, we must calculate based on arrival rate, shopping time, and checkout lines. However, we need additional data on checkout capacity and store occupancy to provide an exact figure.

Step-by-step explanation:

Calculating the Number of Customers in Piggly Wiggly at Any Given Time

To calculate the number of customers in Piggly Wiggly at any given time, we must consider the rate at which customers enter the store and the average time they spend inside, including shopping and checkout time. With customers entering at a rate of 48 customers per hour and spending an average of 20 minutes selecting their groceries, we can determine the average number of minutes between successive arrivals and the time it takes for a specific number of customers to arrive.

Arrival and Shopping Time

Since there are 60 minutes in an hour and customers arrive at a rate of 48 per hour, on average, we expect one customer to arrive every 1.25 minutes. Given that each customer spends 20 minutes shopping on average, we simply multiply the arrival rate by the shopping time to find the average number of customers shopping at any moment.

Checkout Time

For the checkout time, we have two different types of lines, express and non-express. About 25% of all shoppers use the express line which has an average of 2 shoppers in line, while the remaining 75% use the non-express line, averaging 6 shoppers. Adding the average number of shoppers queuing in the express line to the total yields the overall number of customers.

Conclusion

Considering the shopping time and checkout time together, and assuming that the in-store customer count does not exceed the capability of the checkout process to keep it balanced, we can determine the number of customers in the store at any given time. Unfortunately, additional data like the checkout process capacity and the store's maximum occupancy limit are needed to provide a precise answer.