Question 1200113: A manufacturer uses 1000 items uniformly throughout the year. The cost to produce the items in-house is $40 for set-up and $5.20 per item. Insurance and taxes are estimated as 12% of average inventory, and it costs $0.80 to store each unit for one complete year. How many of these items should the manufacturer produce at a time?
Answer by textot(100)   (Show Source):
You can put this solution on YOUR website! **1. Define Variables**
* **D:** Annual demand (1000 items)
* **S:** Setup cost per order ($40)
* **H:** Holding cost per unit per year
* H = Unit cost * Holding cost percentage + Storage cost per unit
* H = $5.20 * 0.12 + $0.80
* H = $1.424
**2. Calculate Economic Order Quantity (EOQ)**
* EOQ = √(2DS / H)
* EOQ = √(2 * 1000 * 40 / 1.424)
* EOQ = √(80000 / 1.424)
* EOQ ≈ 237.17
**Therefore, the manufacturer should produce approximately 237 items at a time to minimize the total cost.**
**Key Concepts**
* **Economic Order Quantity (EOQ):** This model helps determine the optimal order quantity that minimizes the total cost of inventory, which includes ordering costs and holding costs.
* **Ordering Costs:** Costs associated with placing an order (e.g., setup costs, administrative costs).
* **Holding Costs:** Costs associated with storing inventory (e.g., storage space, insurance, taxes, obsolescence).
This analysis assumes that demand is constant and known, and that lead time (time between placing an order and receiving it) is negligible.
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