A Monte Carlo Analysis question: An online apparel retailer will sell winter coa

Question

A Monte Carlo Analysis question: An online apparel retailer will sell winter coats this season. The retailer purchases the coats from a supplier at a cost of $175 and will sell them for $250. Demand has been forecasted to be 2,000 coats this season, but is not known for certain and could range anywhere from 1,000 to 3,000 coats. At the end of the season, the retailer will have a 1/2 off sale in order to clear out the inventory. (a) Assume a uniform distribution for demand. Assume the retailer orders 2,000 coats. Construct a simulation of 1,000 trials to evaluate the distribution of profit. What is average profit over your trials? What is the confidence interval within which profit is likely to fall 95% of the time? (b) Graph the distribution of profit in your simulation. How does it differ from the uniform distribution? (c) Simulate order sizes in 50-unit increments from 1,500 coats to 2,500 coats. Determine the order size that appears to maximize expected profit. Is this order size equal to average demand? Why or why not?

Can you please provide detailed solutions, including graphs.

Thank you.

Explanation / Answer

Assuming uniform distribution for demand. Number of coats ordered by retailer=2000. Cost Price of coat= $175 Selling Price of coat= $250 Profit= $250- $175 = $75 Net profit for 1000 coats= 1000*$75= $75000 The confidence interval within which profit is likely to fall 95% of the time is the end of the season. Distribution of profit differs from the uniform distribution in the way that profit is not uniformly distributed . At the end of the season profit declines to a great extent. This decline in uniformity leads to the dwindling profit. Order sizes in 50-unit increments from 1,500 coats to 2,500 coats. The order size that appears to maximize expected profit should be around 1900. This quantity leads to the uniformity of profit

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