If instead of weighting the problem by the population of each city, assume that the analysis was done with each city having equal weight. That is, what matters is how close a city is to the capital, not how many people live there.
a) Which capital location is now the best from an average-distance point of view?
b) Which capital is now the best in terms of the number of cities within 100, 200, and 300 miles?
c) Does this make the analysis easier or harder? Why?