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(Note: postscript files can be viewed with ghostview and printed with lpr.)dx/dt = kx(M-x)-h.
Here M is the carrying capacity of the lake, kM is the natural growth rate, and h is the rate at which fish are being harvested.
(a) What is the largest sustainable yield h? (I.e. what is the largest h such that there are solutions to the above equation with x>0 for all t>0.) Call this h_max. This number depends on k and M.
(b) Give a rough sketch of the solution curves for h less than h_max, h=h_max, and h greater than h_max.
(c) If this is an approximate model of a real-world lake, is it a good idea to fish near the maximum sustainable rate h_max? Explain.
Last updated: Mar. 3, 1999.