A retail chain plans to sell bottles of a special holiday drink this season. The bottles are typically stocked one month in advance and sold before the holiday for full price. After the holiday, the leftover bottles would be marked down to get sold. For each bottle, the item cost is $3.85, the full selling price is $11.99, and the marked down price is $0.98. Historically, demand is normally distributed with a mean of 1.28 million bottles and a standard deviation of 0.04 million bottles. You would need to show equations, steps, and the final results with units for full credits. Answers are in millions using 5 decimals, e.g. 1.76384 million bottles. You should not round up the numbers! For simplicity, all taxes and other costs are not considered. All parts below are based on the optimal quantity decision found in part (a). (a) To maximize expected profit, how many bottles should the retailer carry this year? (b) What are the expected inventory and the corresponding expected sales? (c) What is the expected profit? (in millions of dollars with 5 decimals) (d)Based on part (b), state the in-stock probability. Then, find the stockout probability. (e) Sketch the normal demand distribution with details to illustrate the business situation. Make sure to show the optimal quantity, the service level, the in-stock probability, and the stockout probability with numerical values. Hint: You can use the following table to lookup for z value and the corresponding I(z) value:
A retail chain plans to sell bottles of a special holiday drink this season. The bottles are typically stocked one month in advance and sold before the holiday for full price. After the holiday, the leftover bottles would be marked down to get sold. For each bottle, the item cost is $3.85, the full selling price is $11.99, and the marked down price is $0.98. Historically, demand is
You would need to show equations, steps, and the final results with units for full credits. Answers are in millions using 5 decimals, e.g. 1.76384 million bottles. You should not round up the numbers! For simplicity, all taxes and other costs are not considered. All parts below are based on the optimal quantity decision found in part (a).
(a) To maximize expected profit, how many bottles should the retailer carry this year?
(b) What are the expected inventory and the corresponding expected sales?
(c) What is the expected profit? (in millions of dollars with 5 decimals)
(d)Based on part (b), state the in-stock probability. Then, find the stockout probability.
(e) Sketch the normal demand distribution with details to illustrate the business situation. Make sure to show the optimal quantity, the service level, the in-stock probability, and the stockout probability with numerical values.
Hint: You can use the following table to lookup for z value and the corresponding I(z) value:
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