Ice Cream Vendors at the Beach
Warning: This is a difficult problem set. Print it out, read it, and think about it. Allow yourself enough time to get it done.
Along a stretch of beach 'down the shore' there are 500 children in five clusters of 100 each. They are clustered in this fashion due to the location of the lifeguard stands. The stands are labeled A, B, C, D, E. Each child buys one ice cream cone per day.
There are two rival ice cream vendors named Ben and Jerry. Each morning they roll there wagons down to the beach for business at 10 AM. They must locate their wagon at the exact location of one of the clusters. The children always go to the nearest vendor. If there is a vendor in a cluster then all 100 children buy from that vendor. For clusters without a vendor, 50 of the children will walk to an adjacent cluster with a vendor for ice cream, only 20 will walk as far as two clusters, none will walk three or more clusters for ice cream. If both Ben and Jerry are located in the same cluster then they each get 50% of the demand for ice cream at that cluster. If Ben and Jerry locate in different clusters then children that are equidistant from both of them will be equally split.