At a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population y: the more fish there are, the easier it is to catch them. Thus we assume that the rate at which fish are caught is given by Ey, where E is a positive constant, with units of 1/time, that measures the total effort made to harvest the given species of fish. To include this effect, the logistic equation is replaced by (20) dydt=r(1−yK)y−Ey This equation is known as the Schaefer model after the biologist M. B. Schaefer, who applied it to fish populations. Determine E so as to maximize Y and thereby find the maximum sustainable yield Ym.
At a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population y: the more fish there are, the easier it is to catch them. Thus we assume that the rate at which fish are caught is given by Ey, where E is a positive constant, with units of 1/time, that measures the total effort made to harvest the given species of fish. To include this effect, the logistic equation is replaced by (20) dydt=r(1−yK)y−Ey This equation is known as the Schaefer model after the biologist M. B. Schaefer, who applied it to fish populations. Determine E so as to maximize Y and thereby find the maximum sustainable yield Ym.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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At a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population y: the more fish there are, the easier it is to catch them. Thus we assume that the rate at which fish are caught is given by Ey, where E is a positive constant, with units of 1/time, that measures the total effort made to harvest the given species of fish. To include this effect, the logistic equation is replaced by
(20)
dydt=r(1−yK)y−Ey
This equation is known as the Schaefer model after the biologist M. B. Schaefer, who applied it to fish populations.
Determine E so as to maximize Y and thereby find the maximum sustainable yield Ym.
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