## Question

# Consider a parcel of land that contains an even ages stand of trees currently of age in A in t=0. you have to decide how

Consider a parcel of land that contains an even ages stand of trees currently of age in A in t=0. you have to decide how much longer to allow this stand to grow given that when you cut the stand, you incur a cost of c > 0 independent of the age of the stand, and you plan to sell the land for a previously contracted rice of v > 0. If the tree is allowed to grow another T years, the volume of merchantable timber will be Q(T)= e^a-b/(A + T).

The unit price of timber, also independent of, is given by P>0. you seek the value that will maximize (T) = ( P e^a-b/(A =T)- c + v)^-delta T.

Suppose that a=13, b=185, A=40, P=1.78, c=1,000, = .05, and v=2,000. What is the value of T that maximizes (T)? Plot (T) for T=, 1,2,.....,50, = 0.0001, to make sure that you have found a global maximum.

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