MathDB
trawler is about to fish in territorial waters of a neighboring country

Source: Polish MO Finals 1976 p5

August 23, 2024
combinatoricsprobability

Problem Statement

A trawler is about to fish in territorial waters of a neighboring country, for what he has no licence. Whenever he throws the net, the coast-guard may stop him with the probability 1/k1/k, where kk is a fixed positive integer. Each throw brings him a fish landing of a fixed weight. However, if the coast-guard stops him, they will confiscate his entire fish landing and demand him to leave the country. The trawler plans to throw the net nn times before he returns to territorial waters in his country. Find nn for which his expected profit is maximal.