A contractor maintains an average inventory of $75,000 in materials with an annual holding cost rate of 18%. If the annual demand is $450,000 and the ordering cost is $200 per order, how many orders should be placed per year to minimize total inventory costs?
Correct Answer
B) 18 orders
Using EOQ formula: Annual demand = $450,000, Ordering cost = $200, Holding cost = $75,000 × 0.18 = $13,500. EOQ = √(2×450,000×200/13,500) = √13,333 ≈ $25,000 per order. Orders per year = $450,000/$25,000 = 18 orders.
Why This Is the Correct Answer
Option C is correct because it uses the Economic Order Quantity (EOQ) formula to find the optimal order size, then divides annual demand by that order size. The EOQ formula minimizes total inventory costs by balancing ordering costs against holding costs. When calculated properly: EOQ = √(2×$450,000×$200/$13,500) = $25,000 per order, resulting in $450,000/$25,000 = 18 orders per year.
Why the Other Options Are Wrong
Option C: 15 orders
15 orders would result in order quantities of $30,000 each, which is still larger than the optimal EOQ of $25,000, leading to higher than necessary holding costs.
Option D: 12 orders
20 orders would mean smaller order quantities ($22,500 each), which increases ordering frequency and total ordering costs beyond the optimal balance point.
Memory Technique
Remember 'EOQ = Square root of (2 × Demand × Order cost / Holding cost)' with the mnemonic '2 Dogs Over House' for the formula structure, then always divide total demand by EOQ result to get number of orders.
Reference Hint
Look up 'Inventory Management' or 'Economic Order Quantity (EOQ)' in construction business management or project management reference materials, typically found in cost control chapters.
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