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##### Two Problems Assignment

**Description**

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**Question**

1. Dotz?s Bakery bakes fresh apple pies each morning for sale that day. A pie costs $2.00 to make and sells for $4.00. Any pies left at the end of the day are sold at that time to another organization at a discounted price of $1.50. Based on her past experience, the bakery?s manager expects to sell between 10 and 12 pies per day. Based on historical sales records, the bakery manager estimates the probabilities of the different apple pie demand levels as the following;# of Pies 10 11 12;Probability 0.30 0.35 0.35;a) Construct the decision tree that can be used to determine how many pies the bakery should bake daily.;b) Determine the number of pies to bake to maximize the expected daily profits.;c) Suppose the bakery is uncertain about the probabilities provided in the problem. It is all right with the probability for the demand for 10 pies being 0.30 and does not believe this should be changed. It is not certain about the probabilities for the demand for 11 and 12 pies each being 0.35. What are the probabilities for selling 11 pies and for selling 12 pies that make the expected profit for the 11 pie decision equal to the expected profit for the 12 pie decision?;2. Holding goods in inventory is costly because inventoried goods are susceptible to breakage and other forms of physical damage. Typically, the amount of damage (in dollars) increases with the level of inventory (expressed in dollars), but some of the damage is unrelated to the amount of inventory. The following data show a company?s inventory damage experience.;Period Inventory Level (Millions of Dollars) Damage (Thousands of Dollars) Average Age of Inventory (Days);1 $11 $80 31;2 $15 $90 45;3 $13 $70 98;4 $10 $60 15;5 $7 $50 25;6 $9 $70 31;7 $13 $80 82;You are interested in developing a forecast for the Damage for period 9.;a) You believe that there is a cause-and-effect relationship between damage and the inventory level. You believe that the damage is a function of the inventory level. Develop and provide the linear regression equation for the damage given the inventory level using the appropriate independent and dependent variables.;b) How good is the relationship you found in a)? Based on the considerations used during class related to the strength of the relationship, would you recommend using this relationship? Explain your reasoning.;c) If the forecasted inventory level for period 9 is $15,000,000, what is the forecasted damage for Period 9?;d) Your boss believes that there might be a cause-and-effect relationship between damage and the average age of the inventory. He wonders if the damage level might be influenced by the average age of the inventory. Based on the information provided, what would you tell him? Explain your answer. If you do agree with your boss, what would you forecast the damage level for inventory with an average age of 60 days?

Paper#28826 | Written in 18-Jul-2015

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