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Unformatted text preview: IEOR 162, Spring 2012 Homework 04 1. (10 points) A manufacturer is selling a product to two different types of retailers. Among all retailers, 40% are type1 retailers and 60% are type2 retailers. A type1 retailers can sell this product at R 1 = $20 per unit. A type2 retailers can sell this product at R 2 = $15 per unit. We refer to a pair of payment and quantity ( p, q ) as a “contract”. For example, if a retailer chooses ( p, q ) = ($200 , 15), the manufacturer will sell 15 units to the retailer and obtains $200 from the retailer. Therefore, if a type i retailer chooses a contract ( p, q ), his profit is R i q p . The production cost of this product is $10 per unit. Therefore, if a type i retailer chooses a contract ( p, q ), the manufacturer will generate a profit p 10 q from the retailer. The manufacturer intends to announce two contracts ( p 1 , q 1 ) and ( p 2 , q 2 ) to maximize her expected profit while satisfying (i) a type i retailer will be willing to choose contract (...
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 Spring '07
 Zhang
 Optimization, retailer, nonnegative proﬁt

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