Consider a supply chain with a manufacturer (M) and a retailer (R). The manufacturer produces a product A at a cost of c = $50. The manufacturer offers the product to the retailer at a wholesale price of w = $70, and fixes the sale price to p = $90. The market demand is normally distributed with mean of 10,000 units and standard deviation of 1000. Answer the following questions: a. What is the optimal order quantity for the retailer? b. What is the optimal order quantity if the wholesale price is changed to $60? Does the optimal order quantity increase or decrease compared to 1a? Why? c. What is the optimal order quantity if the wholesale price is changed to $80? Does the optimal order quantity increase and decrease compared to 1a? Why?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...
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Consider a supply chain with a manufacturer (M) and a retailer (R). The manufacturer produces a product A at a cost of c = $50. The manufacturer offers the product to the retailer at a wholesale price of w = $70, and fixes the sale price to p = $90. The market demand is normally distributed with mean of 10,000 units and standard deviation of 1000. Answer the following questions:

a. What is the optimal order quantity for the retailer?
b. What is the optimal order quantity if the wholesale price is changed to $60? Does the optimal order quantity increase or decrease compared to 1a? Why?
c. What is the optimal order quantity if the wholesale price is changed to $80? Does the optimal order quantity increase and decrease compared to 1a? Why?
d. If the actual market demand is equal to the mean demand, then what are the profits of the manufacturer and the retailer?
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