MathDB

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/k

, where

k

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

n

times before he returns to territorial waters in his country. Find

n

for which his expected profit is maximal.

5

Problems(1)