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The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 600 units, S= $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?

The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 600 units, S= $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual 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
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The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 600 units, S= $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?
**Problem Description:** The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are as follows: - Annual demand (D) = 600 units - Ordering cost (S) = $20/order - Inventory carrying cost rate (I) = 30% of the item price The price is established by the following quantity discount schedule: | Quantity | Price | |------------|--------------| | 1 to 49 | $5.00/unit | | 50 to 249 | $4.50/unit | | 250 and up | $4.10/unit | **Question:** What should the order quantity be in order to minimize the total annual cost? **Explanation:** To determine the optimal order quantity that minimizes the total annual cost, consider both the cost of the items and the inventory carrying and ordering costs. The discount schedule indicates that purchasing larger quantities results in a lower price per unit. Calculating the total cost for each price tier, including the associated inventory costs, will help determine the most cost-effective order quantity.
Transcribed Image Text:**Problem Description:** The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are as follows: - Annual demand (D) = 600 units - Ordering cost (S) = $20/order - Inventory carrying cost rate (I) = 30% of the item price The price is established by the following quantity discount schedule: | Quantity | Price | |------------|--------------| | 1 to 49 | $5.00/unit | | 50 to 249 | $4.50/unit | | 250 and up | $4.10/unit | **Question:** What should the order quantity be in order to minimize the total annual cost? **Explanation:** To determine the optimal order quantity that minimizes the total annual cost, consider both the cost of the items and the inventory carrying and ordering costs. The discount schedule indicates that purchasing larger quantities results in a lower price per unit. Calculating the total cost for each price tier, including the associated inventory costs, will help determine the most cost-effective order quantity.
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