Using MATLAB, Answer the following problems.

NOTE: If you are not sure, please DO NOT answer.

1. Constant Effort Harvesting. 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 H(y, t) = Ey, where E is a pos- itive constant, with units of 1/time, that measures the total effort made to harvest the given species of fish. With this choice for H(y, t), Eq. (1) becomes dy/dt =r(1 y/K)y Ey. This equation is known as the Schaefer model after the biologist M. B. Schaefer, who applied it to fish populations. (a) Show that if E 0. (b) Show that y = y, is unstable and y = y2 is asymptotically stable. (e) A sustainable yield Y of the fishery 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. The graph of this function is known as the yield effort curve. (d) Determine E so as to maximize Y and thereby find the maximum sustainable yield Ym