A particular forest has growth parameters given by gi = 1 i for i = 1, 2, 3,...,n 1

Chapter 10, Problem T1

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A particular forest has growth parameters given by gi = 1 i for i = 1, 2, 3,...,n 1, where n (the total number of height classes) can be chosen as large as needed. Suppose that the value of a tree in the kth height interval is given by pk = a(k 1) where a is a constant (in dollars) and is a parameter satisfying 1 2. (a) Show that the yield Yldk is given by Yldk = 2a(k 1)1s k (b) For = 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 use a computer to determine the class number that should be completely harvested, and determine the optimal sustainable yield in each case. Make sure that you allow k to take on only integer values in your calculations. (c) Repeat the calculations in part (b) using = 1.91, 1.92, 1.93, 1.94, 1.95, 1.96, 1.97, 1.98, 1.99 (d) Show that if = 2, then the optimal sustainable yield can never be larger than 2as. (e) Compare the values of k determined in parts (b) and (c) to 1/(2 ), and use some calculus to explain why k 1 2