Question: You are in charge of deciding the purchased amount of an item with limited time window for sales and uncertain demand. The unit purchase cost is $10 per item, the selling price is $16, and unsold items at the end of the sales window have a salvage value of $7 per item. Demand is also influenced by the level of competition. If there is none, demand is uniformly distributed between 1200 and 2200 items. However, if a strong competitor enters the game, demand is uniformly distributed between 100 and 1100 items.
• If the probability that the competitor enters the market is assumed to be 50%, how many items should you order to maximize expected profit? (Let us assume that selling prices are the same in both scenarios.)
• What if this probability is 20%? Does purchased quantity increase or decrease?