You are the manager of a forest product company with land recently replanted with a fast-growing species of pine. The merchantable volume of timber at time t is given by Q(t) = at + bt2 − dt3, where a = 10, b = 1, d = 0.01. a) What is the rotation length that maximizes the mean annual increment (Q(T)/T) and what is the associated volume? b) If the net price per unit volume is p = 1 and the discount rate is δ = 0.05, what is the optimal length, volume at harvest, and present value of profits (πS(TS)) for a single rotation? Does your answer satisfy the FOC, [Q′(T)/Q(T)]= δ ?
You are the manager of a forest product company with land recently replanted with a fast-growing species of pine. The merchantable volume of timber at time t is given by Q(t) = at + bt2 − dt3, where a = 10, b = 1, d = 0.01. a) What is the rotation length that maximizes the mean annual increment (Q(T)/T) and what is the associated volume? b) If the net price per unit volume is p = 1 and the discount rate is δ = 0.05, what is the optimal length, volume at harvest, and present value of profits (πS(TS)) for a single rotation? Does your answer satisfy the FOC, [Q′(T)/Q(T)]= δ ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1:
You are the manager of a forest product company with land recently replanted with a fast-growing species of pine. The merchantable volume of timber at time t is given by Q(t) = at + bt2 − dt3, where a = 10, b = 1, d = 0.01.
a) What is the rotation length that maximizes the mean annual increment (Q(T)/T) and what is the associated volume?
b) If the net price per unit volume is p = 1 and the discount rate is δ = 0.05, what is the optimal length, volume at harvest, and present value of profits (πS(TS)) for a single rotation? Does your answer satisfy the FOC,
[Q′(T)/Q(T)]= δ ?
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