Economic Order Quantity (EOQ) formula If A = items consumed per year, P = procurement cost per order, and C = annual carrying cost per item, which expression gives the economic ordering quantity?

Introduction / Context:
The Economic Order Quantity (EOQ) model balances ordering cost and inventory carrying cost to find the lot size that minimizes total annual inventory cost for stable demand items.

Given Data / Assumptions:

• A = annual demand (units per year).
• P = procurement (ordering) cost per order.
• C = annual carrying cost per unit.
• Demand and lead time are constant, shortages are not allowed.

Concept / Approach:
Total annual cost = ordering cost + carrying cost. Ordering cost decreases with larger lots, while carrying cost increases. The optimum occurs where the two are equal in magnitude.

Step-by-Step Solution:
Let Q be the order quantity.Ordering cost per year = (A / Q) * P.Average inventory = Q / 2 (no safety stock assumed).Carrying cost per year = (Q / 2) * C.Total cost TC = (A / Q) * P + (Q / 2) * C.Differentiate TC with respect to Q and set derivative = 0 for minimum.Solving gives Q = sqrt(2 * A * P / C).

Verification / Alternative check:
At EOQ, ordering cost equals carrying cost: (A / Q) * P = (Q / 2) * C which rearranges to Q = sqrt(2 * A * P / C).

Why Other Options Are Wrong:
Options (b), (d), and (e) invert terms incorrectly. Option (c) omits the square root and would not minimize TC.

Common Pitfalls:
Forgetting that C is per-unit per-year, ignoring quantity discounts, or applying EOQ where demand is highly erratic can lead to poor results.

Final Answer:
EOQ = sqrt(2 * A * P / C)