Inventory control (EOQ calculation): When the ordering (purchase) cost is $20 per order, the annual holding (maintenance) cost is $0.50 per unit per year, and annual sales/demand are 20 units, what is the Economic Order Quantity (EOQ)?

Introduction / Context:
The Economic Order Quantity (EOQ) model balances ordering cost and holding cost to find the order size that minimizes total inventory cost. It is widely used in production and retail environments when demand is steady and costs are known. This problem provides the inputs and asks for the EOQ value.

Given Data / Assumptions:

• Ordering (setup) cost per order S = 20 dollars.
• Annual holding cost per unit H = 0.50 dollars per unit per year.
• Annual demand D = 20 units.
• EOQ formula: Q* = sqrt( (2 * D * S) / H ).
• Assume no quantity discounts, constant demand, and instantaneous replenishment.

Concept / Approach:
EOQ minimizes total cost TC(Q) = (D/Q) * S + (Q/2) * H. Differentiating and setting derivative to zero yields Q* = sqrt(2DS/H). We substitute the given D, S, and H to compute the exact order size in units.

Step-by-Step Solution:

Verification / Alternative check:
Rough check: Very low demand (20) with low holding cost (0.50) and moderate order cost (20) can still produce an EOQ larger than annual demand because the model minimizes cost of orders versus holding; with such low H, holding additional units is inexpensive, favoring larger orders.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing “purchase cost” with unit purchase price in the EOQ formula; here “purchase cost” refers to ordering/setup cost per order S, not the item price.

Final Answer:
40