Q.A company uses 1,800 units of a component annually. The cost of placing one order is ₹400 and the carrying cost is ₹16 per unit per annum. Calculate the Economic Order Quantity and the number of orders to be placed during the year.

A second EOQ problem with different figures, including the number of orders the business would place per year.

Step 1 — Compute EOQ:

EOQ = √(2 × A × O ÷ C) = √(2 × 1,800 × 400 ÷ 16) = √(14,40,000 ÷ 16) = √90,000 = 300 units

(since 300 × 300 = 90,000, the square root is exact)

Step 2 — Number of orders per year:

Number of orders = Annual Consumption ÷ EOQ = 1,800 ÷ 300 = 6 orders

Verification using the cost-equality property:

Total Ordering Cost = 6 orders × ₹400 = ₹2,400

Average stock = EOQ ÷ 2 = 300 ÷ 2 = 150 units; Total Carrying Cost = 150 × ₹16 = ₹2,400

Both total costs equal ₹2,400, confirming the EOQ of 300 units is correct. …

A common slip is dividing Annual Consumption by the wrong figure (e.g. by the ordering cost) to find the number of orders — the number of orders is always Annu …