If you think of the distance any individual consumer needs to travel as a penalty&#x2F;loss to that consumer, locating both shops right next to each other at the center clearly does not minimize the sum penalty to the set of consumers.<p>Moving each shop 1% of the distance away from the center will reduce by that amount the distance travelled by nearly every consumer. (Only those consumers located at or between the shops will be harmed, and everyone else will gain. As you continue to move the shops apart, this set becomes larger until you reach an equilibrium.)