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Question
An electronic item retail orders a newly introduced smartphone from a manufacturer at $650 per unit and sells it at $750. The unit production cost at manufacturer level is $400. The retailer knows that a year later, when the manufacturer launches another latest smartphone, the current smartphone cannot be sold at its current price. Instead, they have to sell it at a discounted price $300. From the historical data, the retailer knows that the sales of a smartphone are normally distributed with the average sales of a newly introduced smartphone is 1200 units with a standard deviation of 450 units
1. Determine the retailer's optimal order quantity as well as its expected profit.
2. Determine the manufacturer's expected profit.
3. Supposed that both parties are agreed in a centralized setting, determine the optimal order quantity as well as the supply chain's profit.
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