Checkout Lines

Since the question states that Little’s law can be applied to any single part of the store (for example, just the checkout line, then the average number of shoppers, $N$ , in the checkout line at any time is $N=rt$ , where $r$ is the number of shoppers entering the checkout line per minute and $t$ is the average number of minutes each shopper spends in the checkout line. Since $84$ shoppers per hour make a purchase, $84$ shoppers per hour enter the checkout line. However, this needs to be converted to the number of shoppers per minute (in order to be used with $t=5$ ). Since there are $60$ minutes in one hour, the rate is $\dfrac{84 \quad shoppersperhour}{60 \quad minutes}=1.4 \quad shoppersperminute$ . Using the given formula with $r=1.4$ and $t=5$ yields

$N=rt=(1.4)*(5)=7$

Therefore, the average number of shoppers, N, in the checkout line at any time during business hours is 7.