Suppose a distressed call is made to a Coast Guard Station from a pleasure cruise that is sinking. The distress call is garbled so that all that can be made out is that the sinking ship is near an island. Unfortunately, there are two islands (call them #1 and #2) that could be the approximate location of the sinking ship. Island #1 is ten miles to the south of the Coast Guard Station and Island #2 is ten miles to the north of the Coast Guard Station. Since time is of essence, the Coast Guard Station commander splits his fleet of n boats and orders his boats to search water off of both islands. Because of the time of day, the commander thinks that the probability that the sinking ship is at Island #1 is p1 and the probability that the sinking ship is at Island #2 is p2 = 1p1. Assume that each search boat has probability ps of finding the sinking ship if it is sent to the correct island, and that all search boats act independently. How should the commander divide his fleet of search boats in order to maximize the probability (P ) of finding the sinking ship? In other words, determine (in terms of p1, p2 and ps) the number of boats (call it n1) that should be sent to Island #1 and the number of boats (call it n2 = nn1) that should be sent to Island #2 so that the probability of finding the sinking ship is a maximum. Then determine your values of n1 and n2 for the numerical case in which p1 = 2/5, p2 = 3/5, ps = 1/10, and n = 10, and also determine Pmax.