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Question 2 (35 pts): Caramel also sells various pastries. One popular item is cupcakes that are supplied from a local bakery daily. Nick buys each cupcake at $2.5 and sells it for $6. Daily cupcake demand is normally distributed with a mean of 120 and a standard deviation of 40 . Leftover cupcakes at the end of the day will be sold at a discounted price of $1 per cupcake. Note: The questions in sections (a) - (e) below are independent. That is, in each section use the information given above unless otherwise is stated in that specific section. For instance, in section (b) demand information is given as uniform distribution. In this section use uniform demand distribution. However, in the remaining sections, use the demand information of normal distribution as given in the original question above. a) (7 pts): Given the information above, how many cupcakes should Nick order each morning? b) ( 7pts ): If the demand had a uniform distribution between 100 and 180 , how many cupcakes should Nick order each morning? c) (7 pts): Suppose a customer who is unable to purchase a cupcake (due to stock out), buys a cookie instead. A cookie sells for $2.5 and costs $1 each. Caramel always has some cookies. In this case, how many cupcakes would Nick order each morning? d) (7 pts): Suppose it costs $1 to keep a cupcake in the store for a day. This holding cost is incurred only for the cupcakes that are not sold by the end of the day. In this case, how many cupcakes would Nick order each morning? (ignore part c - no cookie sales, just cupcakes) e) (7 pts): If Nick orders 200 cupcakes in the morning, what is the probability that he will sell all of them by the end of the day

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