Subjects operations research

Economic Order Quantity

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Economic Order Quantity


1. **State the problem:** We need to find the Economic Order Quantity (EOQ) for glass units, given the annual demand, ordering cost, and holding cost per unit. 2. **Given data:** - Annual demand, $D = 2700$ units - Ordering cost, $S = 85$ - Holding cost per unit per year, $H = 4.95$ 3. **Formula for EOQ:** $$EOQ = \sqrt{\frac{2DS}{H}}$$ This formula balances ordering costs and holding costs to minimize total inventory cost. 4. **Calculate EOQ:** $$EOQ = \sqrt{\frac{2 \times 2700 \times 85}{4.95}} = \sqrt{\frac{459000}{4.95}} = \sqrt{92727.27} \approx 304.53$$ 5. **Interpretation:** The EOQ is approximately 305 units (rounded to the nearest whole number). 6. **Note:** The problem asks for EOQ in units, not cases, so no further conversion is needed. **Final answer:** $$\boxed{305}$$ units