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.

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:

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.$

a$.$ Create a line$/$ribbon plot depicting the mean profit as well as an $80\%$ and a $95\%$ confidence interval for GWS$\text{'}$ profit if they create between $2000$ and $15000$ boats, counting by increments of $1000.$

b$.$ Create overlapping density plots depicting the distribution of GWS$\text{'}$ profit, assuming they create $2000,4000,6000,8000,10000,12000,$ or $14,000$ boats.

c$.$ Use simulation optimization to determine the number of boats GWS should produce to maximize:

i$.$ Their expected profit

ii$.$ The $10^("$th $")$ percentile of their profit

iii. The probability that they will earn a profit of at least $$50$ million