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The FedEx Problem

Summary The original shipping strategy of FedEx was to fly all packages to a hub during the afternoon and evening, sort them there, and then fly them to their destinations over night for delivery the next day. This leads to interesting mathematical questions: Given a population represented by points in Euclidean space or on a sphere, what is the location of the hub that minimizes the total distance to all the points? Is such a point unique? After answering these questions, we use census data from 2000 to examine how close the FedEx hub in Memphis is to the proper hub of the U.S. population.