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(b) (9%) Determine the optimal order quantity of the newspaper vendor based on the given demand distribution. Show all your work clearly.

(b) (9%) Determine the optimal order quantity of the newspaper vendor based on the given demand distribution. Show all your work clearly.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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please send solution for part b
A newspaper vendor wants to determine his daily newspaper order while considering uncertainty in customer demand. Specifically, each morning, the vendor must decide how many papers to buy at the wholesale price (0.8 TL). The vendor then sells these papers to the customers during the day at a retail price (2.0 TL) in the amount depending on the demand and available newspaper at hand. At the end of the day, any unsold papers can be sold back to the wholesaler at a scrapped price (0.4 TL). Since the newspaper vendor did not keep track of the past sales data of each day, he can guess a range for possible demand realizations, with the minimum and maximum values as 200 and 260. Due to this lack on information in past data, the newspaper vendor assumes demand is uniformly distributed within this range. (a) (3%) Write down the expected profit function of the newspaper vendor using the cost values specified in the question by specifying the variables. Compute the values of the underage cost and overage cost. (b) (9%) Determine the optimal order quantity of the newspaper vendor based on the given demand distribution. Show all your work clearly. (c) (4%) Consider the case when the retail price changes to 1.5 TL and scrapped price changes to 0.2 TL. Discuss how the underage cost and overage cost will change in this case. Discuss how this change will impact the order quantity you find in part (b) considering these costs (You do not need to calculate the order quantity). (d) (4%) Consider the case when demand has a different distribution, such as Normal distribution with mean = 300 and standard deviation = 20. Does this effect how you find the order quantity in part (b)? If yes, explain how it impacts the solution steps and order quantity clearly (You do not need to calculate the order quantity).
Transcribed Image Text:A newspaper vendor wants to determine his daily newspaper order while considering uncertainty in customer demand. Specifically, each morning, the vendor must decide how many papers to buy at the wholesale price (0.8 TL). The vendor then sells these papers to the customers during the day at a retail price (2.0 TL) in the amount depending on the demand and available newspaper at hand. At the end of the day, any unsold papers can be sold back to the wholesaler at a scrapped price (0.4 TL). Since the newspaper vendor did not keep track of the past sales data of each day, he can guess a range for possible demand realizations, with the minimum and maximum values as 200 and 260. Due to this lack on information in past data, the newspaper vendor assumes demand is uniformly distributed within this range. (a) (3%) Write down the expected profit function of the newspaper vendor using the cost values specified in the question by specifying the variables. Compute the values of the underage cost and overage cost. (b) (9%) Determine the optimal order quantity of the newspaper vendor based on the given demand distribution. Show all your work clearly. (c) (4%) Consider the case when the retail price changes to 1.5 TL and scrapped price changes to 0.2 TL. Discuss how the underage cost and overage cost will change in this case. Discuss how this change will impact the order quantity you find in part (b) considering these costs (You do not need to calculate the order quantity). (d) (4%) Consider the case when demand has a different distribution, such as Normal distribution with mean = 300 and standard deviation = 20. Does this effect how you find the order quantity in part (b)? If yes, explain how it impacts the solution steps and order quantity clearly (You do not need to calculate the order quantity).
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