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

Chapter 10, Problem T2

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A particular forest has growth parameters given by gi = 1 2i 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 . (a) Show that the yield Yldk is given by Yldk = a(k 1) s 2k 2 (b) For = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 use a computer to determine the class number that should be completely harvested in order to obtain an optimal yield, 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) Compare the values of k determined in part (b) to 1 + / ln(2) and use some calculus to explain why k 1 + ln(2)