1. **State the problem:** Calculate the Economic Order Quantity (EOQ), ordering frequency, total costs, and reorder level for an inventory system with given demand, ordering cost, holding cost, and lead time. 2. **Given data:** - Annual Demand $D = 5000$ packs - Ordering Cost per order $C_o = 12000$ - Holding Cost per pack per year $C_h = 4000$ - Weeks in a year = 52 - Lead Time = 3 weeks 3. **Calculate EOQ:** $$\text{EOQ} = \sqrt{\frac{2 \cdot D \cdot C_o}{C_h}} = \sqrt{\frac{2 \cdot 5000 \cdot 12000}{4000}} = \sqrt{30000} \approx 173.205 \text{ packs}$$ 4. **Calculate number of orders per year $N$:** $$N = \frac{D}{\text{EOQ}} = \frac{5000}{173.205} \approx 28.87 \text{ orders}$$ 5. **Calculate frequency of orders in weeks:** $$\text{Frequency} = \frac{52}{N} = \frac{52}{28.87} \approx 1.80 \text{ weeks}$$ 6. **Calculate Total Ordering Cost (TOC):** $$\text{TOC} = \frac{D}{\text{EOQ}} \cdot C_o = 28.87 \times 12000 \approx 346410.16$$ 7. **Calculate Total Holding Cost (THC):** $$\text{THC} = \frac{\text{EOQ}}{2} \cdot C_h = \frac{173.205}{2} \times 4000 = 86.6025 \times 4000 \approx 346410.16$$ 8. **Calculate Total Relevant Inventory Cost (TRC):** $$\text{TRC} = \text{TOC} + \text{THC} = 346410.16 + 346410.16 = 692820.32$$ 9. **Calculate Reorder Level (ROL):** $$\text{Demand per week} = \frac{D}{52} = \frac{5000}{52} \approx 96.15$$ $$\text{ROL} = \text{Demand per week} \times \text{Lead Time} = 96.15 \times 3 = 288.46 \text{ packs}$$ **Final answers:** - EOQ $\approx 173$ packs - Number of orders per year $\approx 28.87$ - Frequency of orders $\approx 1.80$ weeks - Total Ordering Cost $\approx 346410.16$ - Total Holding Cost $\approx 346410.16$ - Total Relevant Inventory Cost $\approx 692820.32$ - Reorder Level $\approx 288$ packs