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A camera store specializes in a particular popular and fancy camera. Assume that these cameras become obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise delivery the next day. In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express service. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they maintain their good reputation. The retail price of the camera is $500, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $50 for each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $400 each. (Assume that the order can only be made at the beginning of the month.) (a) Assume that the demand has a discrete uniform distribution from 15 to 20 cameras a month (inclusive). If 16 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected total cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) What is the expected total cost that corresponds to the optimal order quantity? (d) Assume that the demand can be approximated by a normal distribution with mean 1000 and standard deviation 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost?

A camera store specializes in a particular popular and fancy camera. Assume that these cameras become obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise delivery the next day. In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express service. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they maintain their good reputation. The retail price of the camera is $500, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $50 for each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $400 each. (Assume that the order can only be made at the beginning of the month.) (a) Assume that the demand has a discrete uniform distribution from 15 to 20 cameras a month (inclusive). If 16 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected total cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) What is the expected total cost that corresponds to the optimal order quantity? (d) Assume that the demand can be approximated by a normal distribution with mean 1000 and standard deviation 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost?

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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A camera store specializes in a particular popular and fancy camera. Assume that these cameras become obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise delivery the next day. In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express service. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they maintain their good reputation. The retail price of the camera is $500, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $50 for each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $400 each. (Assume that the order can only be made at the beginning of the month.) (a) Assume that the demand has a discrete uniform distribution from 15 to 20 cameras a month (inclusive). If 16 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected total cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) What is the expected total cost that corresponds to the optimal order quantity? (d) Assume that the demand can be approximated by a normal distribution with mean 1000 and standard deviation 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost?
Transcribed Image Text:A camera store specializes in a particular popular and fancy camera. Assume that these cameras become obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise delivery the next day. In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express service. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they maintain their good reputation. The retail price of the camera is $500, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $50 for each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $400 each. (Assume that the order can only be made at the beginning of the month.) (a) Assume that the demand has a discrete uniform distribution from 15 to 20 cameras a month (inclusive). If 16 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected total cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) What is the expected total cost that corresponds to the optimal order quantity? (d) Assume that the demand can be approximated by a normal distribution with mean 1000 and standard deviation 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost?
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