a) Build a simulation model that allows to evaluate different amounts to be put in liquid investments. Make sure to include the model formulation in the main document (including decision variables, assumptions, auxiliary variables, forecasts and objective). Then, using a Data Table in Excel, evaluate the performance of the following liquid investment amounts (in millions in terms of the final endowment after penalties: 0, 200, 400, 600, 800 and 1000. Run your simulation with at least 10,000 trials. Is this an example of stochastic dominance? Is this an example of risk vs. reward? Explain. What would be your choice for liquid investments among the six ones tested?

b) Use OptQuest to find the optimal amount for liquid investments in terms of the expected final endowment after penalties (which could be neither of the six previous values). Reduce the number of trials to 1,000 when running OptQuest.

c) Add the optimal amount found in (b) to the Data Table found in (a), and re-build the Data Table now with a handful of initial liquid investments (the ones closer to the OptQuest finding). Does the optimal solution found by OptQuest change your conclusion in (b)? Explain.