If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.

The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.

84

Step-by-step explanation:

The key to understanding these problems is having a firm idea about what the variables represent. The variable r, for example, has units of shoppers per minute. This means you will need to divide the number of shoppers by total minutes to calculate variable r.

Example:

“Little’s law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?”

Let’s match units to variables:

“…shoppers spend an average of 5 minutes…” This sounds like the description of variable T. We now know that T = 5 in our problem.

“…approximately 84 shoppers per hour…” is close to the units needed for r; however, r is in shoppers per minute, not hour. To fix this, we convert 84 shoppers / 60 minutes = 1.4. We know that r = 1.4.

We want to know, “…about how many shoppers, on average…,” which are the units for N.

This paragraph was a long-winded way of asking you to solve for N! The actual math involved in this problem looks like the following:

N = rt

N = (1.4)(5)

N = 7

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step-by-step explanation:

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