Q.From the following particulars, calculate the Economic Order Quantity and verify your answer by showing that total ordering cost equals total carrying cost at that quantity:
Annual consumption: 500 units
Ordering cost per order: ₹100
Carrying cost per unit per annum: ₹10

A direct application of the EOQ formula, with the standard cost-equality check that confirms the answer.

Step 1 — Compute EOQ:

EOQ = √(2 × A × O ÷ C) = √(2 × 500 × 100 ÷ 10) = √(1,00,000 ÷ 10) = √10,000 = 100 units

Step 2 — Verify using the cost-equality property (at EOQ, Total Ordering Cost = Total Carrying Cost):

Number of orders per year = Annual Consumption ÷ EOQ = 500 ÷ 100 = 5 orders

Total Ordering Cost = 5 orders × ₹100 per order = ₹500

Average stock held during the year = EOQ ÷ 2 = 100 ÷ 2 = 50 units

Total Carrying Cost = 50 units × ₹10 per unit = ₹500

Since Total Ordering Cost (₹500) exactly equals Total Carrying Cost (₹500), the computed EOQ of 100 units is confirmed as the order quantity that minimises the combined total cost. …

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