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    Question

    An enterprise consumes 25,600 units of a component

    annually. The order cost is ₹600 per order, and carrying cost is ₹12/unit/year. A supplier offers the following discount: • No discount up to 1,800 units • 2% discount for orders ≥ 1,800 units The purchase price is ₹200/unit. Should the firm accept the discount offer?
    A No, EOQ is lower and cheaper Correct Answer Incorrect Answer
    B Yes, total cost is lower at 1,800 units Correct Answer Incorrect Answer
    C No, carrying cost becomes too high Correct Answer Incorrect Answer
    D Indifference point lies beyond 2,000 units Correct Answer Incorrect Answer

    Solution

    EOQ = √(2AD/C) = √(2×25,600×600 / 12) = √25,60,000 = 1,600 units So, EOQ = 1,600 units, which is less than 1,800, so the firm won’t get the discount at EOQ. We need to compare: Case A: Order 1,600 units (no discount) Case B: Order 1,800 units (gets 2% discount) Case A: No Discount (Order Quantity = 1,600 units) • Unit Price = ₹200 • Orders/year = 25,600 / 1,600 = 16 • Ordering Cost = 16 × ₹600 = ₹9,600 • Avg Inventory = 1,600 / 2 = 800 • Carrying Cost = 800 × ₹12 = ₹9,600 • Purchase Cost = 25,600 × ₹200 = ₹51,20,000 • Total Cost (No Discount) = ₹51,20,000 + ₹9,600 + ₹9,600 = =₹51,39,200 ✅ Case B: With 2% Discount (Order Quantity = 1,800 units) • Unit Price = ₹200 – 2% = ₹196 • Orders/year = 25,600 / 1,800 ≈ 14.22 → use 14.22 in calculation • Ordering Cost = 14.22 × ₹600 ≈ ₹8,532 • Avg Inventory = 1,800 / 2 = 900 • Carrying Cost = 900 × ₹12 = ₹10,800 • Purchase Cost = 25,600 × ₹196 = ₹50,17,600 Total Cost (With Discount) = ₹50,17,600 + ₹8,532 + ₹10,800=₹50,36,932 The enterprise should accept the discount. It results in a lower total annual

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