GATE 2016 ME (ME2) – Question 64
A company uses 25000 kg of corn flour yearly. Quantity-discount prices are ₹70/kg for 1–749 kg, ₹65/kg for 750–1499 kg and ₹60/kg for 1500 kg or more. Order-processing cost is ₹500 per order. Annual handling and carrying cost is 20% of purchase price per kg. The optimal order quantity is ______ kg.
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Correct answer: 1499 to 1501
Explanation
For all-unit discount price c, annual cost is Dc+DS/Q+0.20cQ/2. EOQ at the cheapest price60 is sqrt(2·25000·500/12)=1443.38kg, below its1500kg threshold, so test1500kg. Its annual cost is1500000+8333.33+9000=1517333.33, below the best costs in the65 and70 tiers. Thus **1500kg** is optimal.