dy/dt = r(1-y/K)y - Ey

r, K, and E are constants.

This is a logistic model of fish population.

a) Show that if E < r, then there are two equilibrium points y1 = 0

and y2 = K(1 - E/r) > 0

Mr F says: By definition, solve 0 = r(1-y/K)y - Ey.
b) Show that y = y1 is unstable and y = y2 is asymptotically stable.

c)A sustainable yield Y of the fisher is a rate at which fish can be caught

indefinitely. It is the product of the effort E and the asymptotically stable

population y2. Find Y as a function of the effort E.

d) Determine E so as to maximize Y and thereby find the maximum sustainable yield Ym.

Any hints of helps are appreciated. I'm having a real hard time with this

.

Thanks in advance!!