Using the Economic Order Quantity (EOQ) model, if annual demand is 2,400 units, ordering cost is $150 per order, and holding cost is $8 per unit per year, what is the optimal order quantity?
Correct Answer
B) 300 units
EOQ = √(2 × Annual Demand × Ordering Cost / Holding Cost) = √(2 × 2,400 × 150 / 8) = √(720,000 / 8) = √90,000 = 300 units. This minimizes the total cost of ordering and holding inventory.
Why This Is the Correct Answer
Option B (300 units) is correct because it follows the EOQ formula precisely. The calculation involves taking the square root of (2 × 2,400 × 150) ÷ 8, which equals √90,000 = 300 units. This represents the optimal balance between ordering costs and holding costs, minimizing total inventory costs for the contractor.
Why the Other Options Are Wrong
Option A: 245 units
245 units is incorrect because it results from an error in the EOQ calculation, likely from miscalculating the numerator or denominator in the formula.
Option C: 275 units
275 units is incorrect and suggests a computational error in applying the EOQ formula, possibly from rounding errors or incorrect substitution of values.
Option D: 325 units
325 units is incorrect and would result in higher total costs than optimal, indicating an error in the square root calculation or formula application.
Memory Technique
Remember 'EOQ = Square root of (2DS/H)' using the mnemonic 'Every Order Quantity = Square root of (2 Dogs Sleeping / House)' to recall the formula structure.
Reference Hint
Look up 'Inventory Management' or 'Economic Order Quantity' in construction management or business operations chapters of your reference materials.
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