onsider a diamond mine manager's problem witht= (1 + t),t= 0,1, ..., 9.

Suppose that10)= 0.Determine the optimal extraction trajectory that maximized the present value of profits, assuming that the discount rate, = 0.05. Use an initial guess oft= 0.1and an initial stock equal to 1. What if we change the value of10)= 1.4? How does the optimal extraction trajectory change?

Now suppose that the discount rate falls to = 0.03. Starting with the same initial guess for harvest (iet= 0.1), use Solver to resolve the problem when10)= 1.4.

How does your answer for optimal extraction compare with the situation when = 0.05? Provide an intuitive explanation for your answer (a couple of type written sentences in ok).

Your spreadsheet should clearly show the following:

1. Initial guess when10)= 0 = 0.03.
2. Solver's solution for10)= 1.4and = 0.03.
3. Solver's solution for10)= 1.4and = 0.05.
4. A chart comparing the optimal harvest and stock trajectories under the two different
5. discount rate values and when10)= 1.4. (Note that this chart will have 4 lines - two for the optimal harvest trajectories and two for the optimal stock trajectories.)