1. **State the problem:** A manufacturer uses 25000 units per year at a uniform rate. We need to find: i) Economic Order Quantity (EOQ) with given costs and no shortages. ii) Reorder level given a lead time of 409 days. 2. **Formulas and explanation:** - EOQ formula when delivery is instantaneous and no shortages allowed: $$EOQ = \sqrt{\frac{2DS}{H}}$$ where: $D$ = demand rate (units/year) = 25000, $S$ = ordering cost per order = ordering + receiving + hauling + inspection = 23 + 22 = 45, $H$ = holding cost per unit per year. - Holding cost $H$ includes: - Interest cost per unit = 0.056, - Deterioration and obsolescence cost per unit = 0.004, - Cost based on max units in inventory = 0.02 per unit. Total holding cost per unit per year: $$H = 0.056 + 0.004 + 0.02 = 0.08$$ - Reorder level formula: $$Reorder\ Level = d \times L$$ where $d$ = daily demand, $L$ = lead time in days. 3. **Calculate EOQ:** $$EOQ = \sqrt{\frac{2 \times 25000 \times 45}{0.08}} = \sqrt{\frac{2250000}{0.08}} = \sqrt{28125000} \approx 5302.78$$ 4. **Calculate daily demand:** Assuming 365 days per year: $$d = \frac{25000}{365} \approx 68.49 \text{ units/day}$$ 5. **Calculate reorder level:** $$Reorder\ Level = 68.49 \times 409 \approx 27992.41$$ **Final answers:** - EOQ $\approx 5303$ units (rounded to nearest whole number). - Reorder level $\approx 27992$ units (rounded to nearest whole number).