Chapter D1.4, Problem 41E

Optimal harvesting rate Let y(t) be the population of a species that is being harvested, for t ≥ 0. Consider the harvesting model y′(t) = 0.008y – h, y(0) = y₀, where h is the annual harvesting rate, y₀ is the initial population of the species, and t is measured in years.

a.    If y₀ ⁼ 2000, what harvesting rate should he used to maintain a constant population of y = 2000, for t ≥ 0?

b.    If the harvesting rate is h = 200/year, what initial population ensures a constant population?