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Can you help me with Number 2 letters D and E? please include matlab command Project 1 PROBLEMS 1. Constant Effort Harvesting. At a given

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Can you help me with Number 2 letters D and E? please include matlab command

Project 1 PROBLEMS 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 Hy, 1) = Ey, where 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(),1), Eq. (1) becomes dy/dt =r(1 - y/K) - Ey. (1) 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. () Show that y = 1 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 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 Y 2. Constant Yield Harvesting. In this problem, we assume that fish are caught at a constant rateh independent of the size of the fish population, that is, the harvesting rate 0.1) . Then y satisfies dy/dt =r(1 - y/K) - h = 0). (ii) The assumption of a constant catch rate h may be reasonable when y is large but becomes less so when y is small (a) Ifh Y, then y 2 asto, but if yo K/4, show that y decreases to zero as ! increases regardless of the value of yo. (e) If h=rK/4, show that there is a single equi- librium point y = K/2 and that this point is semistable. Thus the maximum sustainable yield is hu=rK/4, corresponding to the equilibrium value y=K/2. Observe that he has the same value as Y. in Problem (d). The fishery is considered to be overexploited if y is reduced to a level below K/2

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