Reference no: EM133456313
Assignment:
GWS is a company that 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:
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Demand
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Probability
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2,000-5,000
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35%
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5,001-10,000
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40%
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10,001-14,000
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20%
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14,001-15,000
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5%
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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 (triangular distribution). Perform the following using R.
a. Develop a line/ribbon plot depicting the mean profit as well as an 80% and a 95% confidence interval for GWS' profit if they create between 2000 and 15000 boats, counting by increments of 1000.
b. Develop overlapping density plots depicting the distribution of GWS' 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:
- Their expected profit
- The 10th percentile of their profit
- The probability that they will earn a profit of at least $50 million
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