The population of salmon next year is given by (S) = Ser (1-S/P) , where S is

The population of salmon next year is given by ƒ(S) = Ser^(1-S/P), where S is this year’s salmon population, P is the equilibrium population, and r is a constant that depends upon how fast the population grows. The number of salmon that can be fished next year while keeping the population the same is H(S) = ƒ(S) - S. The maximum value of H(S) is the maximum sustainable harvest.

(a) Show that the maximum sustainable harvest occurs when ƒ′(S) = 1.

(b) Let the value of S found in part (a) be denoted by S₀. Show that the maximum sustainable harvest is given by

Transcribed Image Text:

Sol 1 1 - rS /P -1).