Suppose that in the Hotelling line there are 12 couples (i.e. 24 people), distributed uniformly in every meter of the line. Assume the line is 12 meters long, the left corner start at 0 (where the first couple is) and ends at 12, where the last couple is, with no couple in the middle. There are two firms selling an identical product at the same price, which all people want and need to walk to buy it. Find and explain clearly:

(i) the non-regulated location of the firms;

(ii) the optimal regulated location and compare the total walking distance of all couples in both cases.