[Your work behind your answer for this question should be in your spreadsheet] You are the manager of a forest products company with land recently planted (t = 0) with a fast-growing species of pine. The merchantable volume of timber at instant t 0 is given by Q(t) = t + t2 t3 , where = 10, = 1, and = 0.01.

(a) What is the maximum volume, and when does it occur? What rotation length maximizes mean annual increment [Q(T)/T], and what is the associated volume?

(b) If the net price per unit of volume is p = 1 and the discount rate is = 0.05, what is the optimal single rotation, Ts, volume at harvest Q(Ts), and present value s(Ts)?

(c) If the cost of replanting is c = 150, what is the optimal Faustmann rotation T*, volume at the Faustmann rotation Q(T*), and present value (T*)?

(d) If the price increases to p = 2, what are the new values for Ts and T*? Do the new values make sense relative to their values when p = 1?