To determine the savings in ordering and carrying costs using the Economic Order Quantity (EOQ) formula, we'll follow these steps:

Step 1: Identify the given parameters.

• Demand (D): $775 \text{ crates per month} \times 12 \text{ months} = 9300 \text{ crates per year}$
• Order cost (S): $30 \text{ dollars per order}$
• Carrying cost percentage: $35\%$ of the purchase price
• Purchase price per crate: $8 \text{ dollars}$
• Carrying cost per crate (H): $8 \times 0.35 = 2.8 \text{ dollars per crate per year}$

Step 2: Calculate the EOQ.

The formula for EOQ is: $EOQ = \sqrt{\frac{2DS}{H}}$ Substituting the values: $EOQ = \sqrt{\frac{2 \times 9300 \times 30}{2.8}}$ Calculating the value: $EOQ = \sqrt{\frac{558,000}{2.8}} = \sqrt{199285.71} \approx 446.97$

Step 3: Determine the number of orders required.

• Current ordering quantity: $775 \text{ crates per month} = 9300 \text{ crates per year}$
• Current number of orders: $\frac{9300}{775} = 12 \text{ orders per year}$
• New number of orders with EOQ: $\frac{9300}{446.97} \approx 20.81$ orders per year.

Step 4: Calculate the current annual ordering and carrying costs.

• Ordering cost: $12 \text{ orders} \times 30 \text{ dollars per order} = 360 \text{ dollars}$
• Carrying cost: $\frac{775}{2} \times 2.8 = 1085 \text{ dollars}$
• Total current cost: $360 + 1085 = 1445 \text{ dollars}$

Step 5: Calculate the EOQ-based annual ordering and carrying costs.

• Ordering cost with EOQ: $20.81 \times 30 = 624.3 \text{ dollars}$
• Carrying cost with EOQ: $\frac{446.97}{2} \times 2.8 \approx 625.76 \text{ dollars}$
• Total EOQ cost: $624.3 + 625.76 = 1250.06 \text{ dollars}$

Step 6: Calculate the annual savings.

$\text{Annual savings} = 1445 - 1250.06 = 194.94 \text{ dollars}$

Conclusion:

The firm could save $194.94 annually in ordering and carrying costs by using the EOQ method.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. What is the significance of the Economic Order Quantity (EOQ) in inventory management?
2. How do carrying costs influence the optimal order size in the EOQ formula?
3. What impact does an increase in demand have on the EOQ?
4. How would a change in ordering costs affect the EOQ calculation?
5. What are the limitations of using the EOQ model in real-world scenarios?

Tip: The EOQ model assumes a constant demand rate and ordering costs, which might not always hold true in practice.