Often, when logistics practitioners think about having some automatic way of picking a latitude and longitude, they think about a problem such as where the four cities form a square on a map. In this case, let’s assume that each city has a population of one million, and the latitude and longitude of the four points are (15,155), (15,158), (18,155), and (18,158).
a. What is the latitude and longitude of the physics center of gravity?
b. What is the average distance to each of the cities from this point?
c. Is there a better point that would minimize the weighted-average distance?
d. If the population of City 1 were five million, what would be the physics center of gravity latitude and longitude?