Monte Carlo Simulation

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Optimal Production Quantity by Monte Carlo simulation You have recently taken a position as the engineer in charge of your company’s seasonal product, which is manufactured during the off-season (think surfboards, or skis). You want to determine the optimum production level. If you produce fewer units than you can sell, your profit will not be as large as it could be; if you produce too many units, the unsold units at the end of the season will hurt profits. A review of the company’s records shows that the fixed cost of production (e.g., renting the factory) is $30,000 per season, no matter how many units are made, and that it costs $2000 above the fixed cost to make one unit (variables costs like the raw materials, which vary with the production level). In addition, past sales have been randomly, uniformly distributed over the range from 25 to 50 units per season, with no increasing or decreasing trend in the sales data. Your sales force estimates that you cannot raise the price above $4000 because of the competition. Determine the optimal number of units to produce for each season. Assume a selling price of $4000 during the season. Assume also that at the end of the season all unsold units can be sold at $1000 each. Do this by a statistical analysis of the profit (sales income at the two prices, minus fixed and variable costs) at each of the 26 possible production levels. Step regularly through all the levels from 25-50 units, maybe using a loop. At each production level, first randomly choose n = 50 demand levels to test (this could be done in a regular fashion, but random choice is more generally useful as you will see later). Make a plot of the profit as a function of production level, n. Test larger values of n up to 5000, and see how noisy your plot looks at various values of n. What is the production level that is predicted to give your company the greatest profit?

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I would not deny you the satisfaction of solving this assignment on your own.  But if you make a decent effort to implement a solution and you have specific questions, I might offer some guidance.


Or you could simply click "See Answer" at .