The following information is to be usedfor Questions 6, 7, and 8 J. Durving Wood owns a tract of forested land in Jacquet. The volume of lumber increases with time (t) according to: f(t) -2,500+50t+10r2 The price of a unit of timber from a tree at least 50-years old is $1 (buyers will not purchase 'younger' wood), and is expected to remain so for all time. The annual interest rate which J. Durving can earn on alternate investments is 2.02%, which translates into an instantaneous interest rate (2) of 2%, or .02 6. Suppose that the cost of cutting is trivial, so J. Durving considers it to be zero. Suppose further that J. Durving plans to abandon the land on which the trees are growing after the initial harvest. How long should it wait before cutting, if its goal is to maximize the present value of the stand (i.e., at what age (t) should the trees be cut)? A. ' smaller than 80 years B. at least 80 years but less than 90 years C. at least 90 years but less than 100 years t at least 100 years but less than 110 years D. E. at least 110 years Suppose that the cost of cutting is $5,000 (independent of of the age of the stand, and also independent of the volume of timber) 7. Continue to assume that J. Durving plans to abandon the land on which the trees are growing after the initial timber harvest. How long should it wait before cutting, if its goal is to maximize the present value of the stand (i.e., at what age (t) should the trees be cut)? A. smaller than 80 years B. tat least 80 years but less than 90 years C. f at least 90 years but less than 100 years D. t' at least 100 years but less than 110 years E. at least 110 years 8. The cost of cutting is $5,000 (independent of of the age of the stand, and also independent of the volume of timber) Suppose that J. Durving plans to re-plant trees on the land after it clear-cuts the existing stand of timber The 'site value' (A) of the (bare) land is $22,500. The proceeds of the land sale, net of cutting cost, will be A-c $ 13, 500-5,000-$8,500 How long should J. Durving wait before cutting, if its goal is to maximize the present value of the stand PLUS the net proceeds of the land sale (what is the optimal rotation period, t)? A. 'smaller than 80 years B at least 80 years but less than 90 years C. at least 90 years but less than 100 years D. at least 100 years but less than 110 years E. at least 110 years