Question

There are 100 inhabitants in the village A and 50 inhabitants in the village B. In what point of the road connecting these two villages should be a bathhouse built in order to minimize the total distance passed by all 150 inhabitants to the bathhouse and back?

Answer 1

Let the distance between villages be a. Suppose that the bathhouse is built at a distance x from A (0 ≤ x ≤ a). Then the total distance will be 2(100x + 50(a − x)) = 200x + 100a − 100x = 100x + 100a. It is minimal when x = 0. This means that the bathhouse should be built in the village A.