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A supermarket bakery must decide how many birthday cakes to prepare for the upcoming weekend. Cakes cost $59 each to make, and they sell for $101 each. Unsold cakes are sold at $29.5 on Monday, and typically all the remaining cakes are sold at that price on Monday. Demand is normally distributed with the mean of 151 and standard deviation of 30.2. Determine the followings:

Cost of Shortage (Cs):

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Cost of Excess (Ce):

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What is the optimal service level?

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What is the corresponding z value?

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What is the optimal number of birthday cakes to make for the weekend? (Keep two decimal places in your calculations)

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