solution

Your local sports team has just won the championship, so as the owner of several sporting-goods stores in the area you need to decide how many hats with the team’s logo you should order. Based on past experience, you best estimate of demand (D) within the next month is that it will be between 1000 and 5000 hats. Your supplier will sell you hats at a wholesale unit price of w = $11, and during the peak period you will sell them at a retail price of r = $16.95. If you sell out during the peak period you have no opportunity to re-order more. On the other hand, if you still have hats after the peak period, you mark them down to a clearance price of c = $6.95 and sell them at a loss; assume that you can eventually sell all remaining hats at this clearance price without further mark-downs.

a. How many hats should you order to maximize your profit?

i. Write down the formula for profit.

ii. Perform 100 simulation of the profit when 1,000, 2,000, 3,000, 4,000, and 5,000 hats are ordered respectively. Find mean, standard deviation, best observed, worst observed, 75% and 25% percentile of the profit, probability of earning (profit >0). Draw histograms to show the distribution of profit. Draw box plot of profit for ordering 1,000, 2,000, 3,000, 4,000, and 5,000 hats. Compare the results and discuss your observations.

b. Suppose you had the choice between either hiring a really big person to do some negotiating with your supplier to get the unit wholesale cost down to $9.00 from $11.00, or hiring a slick advertising agency for some ‘image’ hype and thus be able to charge $18.95 unit retail rather than 16.95 during the peak period. Which would be better? Base your comparison on what seems to be the best quantity to order from each of the two alternatives.