A firm purchases 4,000 units of a particular item per annum at ₹40 per unit. Ordering cost is ₹100 per order and inventory carrying cost is 12.5%. Required: (a) Determine optimal order quantity. (b) If a 3% discount is o

(a) Optimal Order Quantity (EOQ) EOQ = √(2AO/C) A = Annual Usage = 4000 units O = Ordering Cost per order = ₹100 C = Carrying Cost = ₹40 × 12.5% = ₹5 EOQ = √(2 × 4,000 × 100) / 5 = 400 units (b) Calculation of total cost for 400 units (Case 1) and 1000 units (Case 2) Ordered Quantity Purchase Price Ordering Cost Carrying Cost Total Cost 400 units (Case 1) 4,000 × ₹40 = ₹1,60,000 (4000/400) × ₹100 = ₹1,000 (400/2) × ₹5 = ₹1,000 ₹1,62,000 1,000 units (Case 2) 4,000 x ₹38.8 (after 3% discount) = ₹1,55,200 (4000/1000) × ₹100 = ₹400 Carrying cost per unit = 38.8 × 0.125 = 4.85 Total carrying cost = (1000/2) x 4.85 = ₹2,425 ₹1,58,025 Since the total cost in case 2 is less than case 1 (existing situation), therefore, firm should accept the offer.