Suppose you own a stand of fast-growing pines. The growth function of the pines is Q(t) = 10t + t?-0.01t, where Q(t) is the volume of timber in year t. a) What is the maximum volume of timber this stand of pines can produce? b) Suppose the difference between the timber price and the harvesting cost is $1, the replanting cost is $150, and the discount rate is 5%. Please find out the optimal rotation interval T*, the volume of timber at T.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose you own a stand of fast-growing pines. The growth function of the
pines is Q(t) = 10t + t2-0.01t3, where Q(t) is the volume of timber in year t.
a) What is the maximum volume of timber this stand of pines can produce?
b) Suppose the difference between the timber price and the harvesting cost is $1, the
replanting cost is $150, and the discount rate is 5%. Please find out the optimal rotation
interval T*, the volume of timber at T*.
Transcribed Image Text:Suppose you own a stand of fast-growing pines. The growth function of the pines is Q(t) = 10t + t2-0.01t3, where Q(t) is the volume of timber in year t. a) What is the maximum volume of timber this stand of pines can produce? b) Suppose the difference between the timber price and the harvesting cost is $1, the replanting cost is $150, and the discount rate is 5%. Please find out the optimal rotation interval T*, the volume of timber at T*.
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