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A retail grocer has a daily demand X for a certain food sold by the pound, such that X (measured in hundreds of pounds) has probability density function

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(He cannot stock over 100 pounds.) The grocer wants to order 100k of food on a certain day. He buys the food at 6¢ per pound and sells it at 10¢ per pound. What value of k will maximize his expected daily profit?

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