https://file.aiquickdraw.com/mathbot/file/1729024117339fg0w53x9.pdf

The document you provided is an optimization worksheet focusing on minimizing total inventory costs by balancing carrying and reordering costs. The scenario discusses a business selling 2,000 computers annually and explores different ordering strategies to minimize these costs. The key goal is to determine the economic order quantity (EOQ), which is the order size that minimizes total inventory costs. The worksheet includes various questions related to average inventory, carrying costs, reordering costs, and the application of calculus to find the optimal order quantity.

Here are some insights from the questions:

- **Question 2**: The average inventory level is typically \( Q/2 \), where \( Q \) is the order quantity.
- **Question 4**: The total carrying cost is \( C \times \frac{Q}{2} \), where \( C \) is the carrying cost per unit per year.
- **Question 5**: The number of orders per year is \( N = \frac{D}{Q} \), where \( D \) is the annual demand.
- **Question 8**: The total cost \( T \) equation combines both carrying and reordering costs: \( T = C \times \frac{Q}{2} + O \times \frac{D}{Q} \), where \( O \) is the cost per order.
- **Question 10**: The EOQ formula is \( EOQ = \sqrt{\frac{2OD}{C}} \).

**Example**: Using the numbers in Question 11 for Sporty Goods:
- \( D = 20,000 \) units, \( O = 500 \), and \( C = 5 \).
- Plugging these into the EOQ formula gives:
\[ EOQ = \sqrt{\frac{2 \times 500 \times 20,000}{5}} = 2000 \text{ units}. \]

Let me know if you'd like detailed explanations for specific questions or further assistance! Would you like to go into more detail or ask about a particular step?

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**Related Questions:**
1. How would the EOQ change if the carrying cost doubled?
2. Why is minimizing total cost important for a business's profitability?
3. What impact does reducing the number of orders have on carrying costs?
4. How could the demand forecast affect the reordering strategy?
5. What is the relationship between carrying cost and order size in this model?

**Tip**: The EOQ formula assumes constant demand and ordering costs; if either changes, you may need to re-evaluate your ordering strategy.

The document provided by the user focuses on optimizing inventory costs through the concept of Economic Order Quantity (EOQ) to balance carrying and reordering costs. The scenario involves finding the optimal strategy for ordering 2,000 computers per year to minimize total inventory costs.

Explore how to minimize total inventory costs through the Economic Order Quantity (EOQ) model. This case study examines ordering strategies for 2,000 computers annually and applies calculus to find the optimal order size. Key mathematical concepts like carrying cost, reordering cost, and optimization techniques are used. Ideal for business students and those studying inventory management.

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