1. (3 pts) 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 $75,000. There will be sufficient demand for all of their remaining stock at the reduced price. They hire a consultant who estimates that at the $150,000 price point demand for the new boats will be somewhere between 2,000 and 15,000, with probabilities as in the table below:[PM1]

Demand	Probability
2,000-5,000	30%
5,001-10,000	45%
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 each boat will be a minimum of $77 thousand and a maximum of $100 thousand, with a most likely value of $90,000[PM2]. Develop four Monte Carlo Simulations, with 100,000 trials each, to calculate their total profit over the two-year period assuming a production quantity of 4,000, 8,000, 12,000, and 15,000 boats.

1. Create a data frame with columns for each uncertain input in the problem.
2. Create a function which takes production quantity as an input and outputs a mutated version of the data frame from (a). The output should add columns for units sold at full price, units sold at the discounted price, total revenue, total cost, and net profit.
3. Use the function from (b) to calculate the mean and standard deviation of net profit and create a histogram of net profit for each of the listed production quantities.