A retail grocer has a daily demand Y for a certain food sold by the pound, where Y

Chapter 4, Problem 4.179

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A retail grocer has a daily demand Y for a certain food sold by the pound, where Y (measured in hundreds of pounds) has a probability density function given by f (y) = 3y2, 0 y 1, 0, elsewhere.(She cannot stock over 100 pounds.) The grocer wants to order 100k pounds of food. She buys the food at 6 per pound and sells it at 10 per pound. What value of k will maximize her expected daily profit?

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