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FunMall buys a kind of Halloween costume from a manufacturer at $31 apiece, and sells the costumes to its customers at $59 apiece. The manufacturer's

FunMall buys a kind of Halloween costume from a manufacturer at $31 apiece, and sells the costumes to its customers at $59 apiece. The manufacturer's production cost is $9 apiece. FunMall estimates the demand is normally distributed with a mean of 3000 and a standard deviation of 1000. After Halloween, FunMall discounts any unsold costumes at $5 apiece. The manufacturer is thinking of offering the following deal to FunMall. After Halloween, FunMall can return any unsold costumes for a refund of $8 apiece. If FunMall decides to return the unsold costumes to the manufacturer, the shipping and handling cost incurred by FunMall is $1 apiece. The manufacturer can sell the returned products to a discounter at $6 apiece. Suppose FunMall accepts the above buy-back contract and orders 3300 pieces of the costumes from the manufacturer, then its expected lost sales, sales and leftover inventory are 267, 2733 and 567, respectively. What is the manufacturer's expected profit?

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