Uncertain Scenario-Maximizing the Mean

The potential revenues of all projects are in fact uncertain. The company determines that the revenue for project 1 is following a uniform distribution ranging from $1,200,000 to $2,000,000.  The revenue for project 2 is distributed normally, with a mean of $1,500,000 and a standard deviation of $200,000.  The revenue for project 3 follows a triangular distribution with a minimum of $1,350,000, maximum of $1,600,000, and it is most likely to be $1,500,000.  The revenue for project 4 is distributed normally, with a mean of $1,800,000 and a standard deviation of $800,000.  The bank wants to find the optimal solution which takes all these uncertainties into account. 

a) In Excel, formulate an LP model for this problem with the objective of maximizing total profit, incorporating all uncertainties. 

b.) Find the optimal solution which can maximize the average uncertain profit.

c.) Past screen shots of your model with formulas, model with solutions, solver setting, simulation setting and the output distribution of the uncertain profit.