A mathematician is a device for turning coffee into theorems.  -Paul Erdos

We have a natural tendency to oversimplify things because it’s easier to make sense of simple things than complex things.  The map on the right represents the simplest view of the relationship between a store and its customers.  The two-mile radius around the store is a reasonable estimate of the trade area for the store, which means that most of the customers will be inside the circle.  If this is true 90% of the time, we don’t care about the details of how customers make their choices.  But what if only 70% of the customers actually are in the circle? 60%? 40%? At some point we have to consider a more complex set of factors that determine our true trade area and whether it contains enough potential customers to make a store successful. Continue reading →