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 offish. To include this effect, the logistic equation is replaced bydy/dt=r(1−y/K)y−Ey.(i)This equation is known as the Schaefer model after the biologist M. B. Schaefer, who applied it to fish populations.(a) Show that ifE0.(b) Show that y=y1 is unstable and y=y2 is asymptotically stable.(c) 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.