Sarah wants to create a special holiday-themed soap. These soaps have an overall production cost of 10$ and will be sold for 15$ each. She forecasts a seasonal demand of 15000 units; however, it is unlikely that demand will be equal to the forecast. Any soap that is left over from the season will have to be sold at a 50% discount. She therefore decides to use the A/F method to build a demand model based on historic forecast/demand pairs from other holidays (see soap.xls). Given this data set, how many soaps should be produced in order to maximize expected profits (i.e., calculate the optimal order quantity).

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A B C Forecast Demand 500 550 5000 4765 20000 22060 7500 7483 3500 3634 1000 721 10000 9044 10000 10789 10000 10001 5200 4929 7300 7203 2400 2554 5400 4543 2400 3289 Average Current Forecast 15000 St. Dev A B C Forecast Demand 500 550 5000 4765 20000 22060 7500 7483 3500 3634 1000 721 10000 9044 10000 10789 10000 10001 5200 4929 7300 7203 2400 2554 5400 4543 2400 3289 Average Current Forecast 15000 St. Dev