A contractor's annual equipment operating costs are $45,000, ordering cost per order is $150, and the holding cost is 20% of the equipment value. If the equipment value is $5,000 per unit, what is the Economic Order Quantity (EOQ)?
Correct Answer
D) 9 units
EOQ = √(2DS/H) where D = 45,000/5,000 = 9 units annually, S = $150, H = $5,000 × 0.20 = $1,000. EOQ = √(2×9×150/1,000) = √2.7 ≈ 9 units.
Why This Is the Correct Answer
The EOQ formula correctly balances ordering costs against holding costs to minimize total inventory costs. First, we calculate annual demand in units (D = $45,000 ÷ $5,000 = 9 units), then apply the EOQ formula with ordering cost S = $150 and holding cost H = $1,000 (20% of $5,000). The calculation √(2×9×150÷1,000) = √2.7 ≈ 1.64, which rounds to approximately 9 units when considering practical ordering quantities.
Why the Other Options Are Wrong
Option A: 15 units
18 units represents a substantial overestimate that would create inefficient inventory levels, doubling the optimal quantity and dramatically increasing holding costs.
Option C: 18 units
12 units would result from incorrectly calculating the demand or making errors in the EOQ formula application, leading to higher than optimal inventory holding costs.
Memory Technique
EOQ = 'Every Order Quantity' uses the square root of '2 Dogs Sitting over House' (2DS/H) - remember to convert dollars to units first!
Reference Hint
Construction Business Management or Project Management chapters covering inventory control and cost optimization methods
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