$1.$ A supermarket has $30$ checkouts. There are currently $50$ customers waiting to go

through the checkouts. Based on historical data, the supermarket manager knows that

it will take, on average, $10$ minutes to process each customer. Using Little$$s Law, how

long will it take to process all the current customers?

$2.$ Over the lunch period, the supermarket is busier, with $70$ customers waiting to go

through checkout. How long will it now take to process all the customers?

$3.$ On this day, however, $3$ checkout staff have called in sick. Recalculate the previous two

scenarios.

$4.$ The supermarket$$s head office has undertaken some research that has discovered that

they are losing customers because of lengthy waiting times at the checkouts. They

have decided that each customer should wait no longer than $10$ minutes at the

checkout and have instructed the supermarket manager to invest in new checkouts on

this basis. Assuming the maximum number of customers queuing at any given time is

$70,$ how many additional checkouts would the supermarket require?