What to submit?

Please submit (i) a word file explaining in detail your answers to each question (you can use screenshots of the R to explain your answers) AND (ii) an R file with a separate tab for each question. For each question, make sure you develop the model and present the simulation results - the R file should be self-explanatory. The assessment of your work will include both the accuracy and the clarity of your word file and the R file. But even if you are struggling with R, we will grade favorably if you demonstrate your understanding of the concepts and how you are planning to solve the problem.

1. GWS is a company that markets outboard motorboats directly to consumers for recreational use. Recently, they've been developing a project they think has a lot of potential: the first mass market boats with electric motors. They haven't started advertising their new product yet, nor have they organized a presale because they don't want to lose their first-mover advantage. As a result, GWS has a limited understanding of the size of the market for their new project. They plan to retail their boats for $150,000, but after two years, when competition enters the market and the novelty factor wears off, they'll have to drop the price to $70,000. They hire a consultant who estimates that at this price point, over the next two years, demand for the new boats will be somewhere between 2,000 and 15,000, with probabilities as in the table below:

Demand	Probability
2,000-5,000	35%
5,001-10,000	40%
10,001-14,000	20%
14,001-15,000	5%

The fixed cost of manufacturing any number of boats is normally distributed, with a mean of $300 million and a standard deviation of $60 million. They estimate that the variable cost to produce one boat will be a minimum of $77 thousand and a maximum of $100 thousand, with a most likely value of $90,000. Develop four Monte Carlo Simulations to calculate their total profit over the two year period assuming they produce

1. 4,000 boats
2. 8,000 boats
3. 12,000 boats
4. 15,000 boats

For each simulation, provide the mean and standard deviation as well as a histogram.