An economic enterprise requires 90,000 units of certain item annually. The cost per unit is Rs. 3. The cost per purchase order is Rs. 300 and the inventory carrying cost is Rs. 6 per unit per year. What is EOQ?

Question

Prepp Team · Accepted Answer

Understanding the Economic Order Quantity (EOQ)

This problem asks us to calculate the Economic Order Quantity (EOQ) for an economic enterprise. The EOQ is a crucial concept in inventory management that helps determine the optimal order quantity to minimize the total inventory costs, which include ordering costs and holding costs.

What is EOQ?

The Economic Order Quantity (EOQ) is the ideal quantity of goods that a company should purchase to minimize inventory costs such as holding costs, shortage costs, and order costs. It is a model designed to find the most efficient inventory level.

EOQ Formula

The standard formula for calculating EOQ is:

$$ EOQ = \sqrt{\frac{2DS}{H}} $$

Where:

D = Annual Demand (in units)
S = Ordering Cost per order
H = Holding or Carrying Cost per unit per year

Note: The cost per unit (Rs. 3 in this case) is not directly used in the basic EOQ formula but is relevant for calculating the total cost of goods or other related metrics.

Applying the EOQ Formula: Step-by-Step Calculation

Let's identify the given values from the problem:

Annual Demand (D) = 90,000 units
Ordering Cost per order (S) = Rs. 300
Inventory Carrying Cost per unit per year (H) = Rs. 6

Now, we substitute these values into the EOQ formula:

$$ EOQ = \sqrt{\frac{2 \times 90,000 \times 300}{6}} $$

First, calculate the numerator:

$$ 2 \times 90,000 \times 300 = 180,000 \times 300 = 54,000,000 $$

Now, divide the numerator by the holding cost (H):

$$ \frac{54,000,000}{6} = 9,000,000 $$

Finally, take the square root of the result:

$$ EOQ = \sqrt{9,000,000} $$ $$ EOQ = 3000 $$

The Economic Order Quantity is 3000 units.

Result

The calculated EOQ is 3000 units. This means that ordering 3000 units at a time will help minimize the total inventory costs (ordering costs plus holding costs) for this enterprise, given the specified demand, ordering cost, and holding cost.

Revision Table: Key Inventory Management Concepts

Concept	Description	Relevance to EOQ
Annual Demand (D)	Total number of units required per year.	Directly proportional to EOQ (in the numerator). Higher demand usually means higher EOQ.
Ordering Cost (S)	Cost incurred each time an order is placed (e.g., administrative costs, shipping fees).	Directly proportional to EOQ (in the numerator). Higher ordering cost favors larger order quantities (higher EOQ) to reduce the number of orders.
Holding Cost (H)	Cost of carrying one unit in inventory for one year (e.g., storage costs, insurance, obsolescence).	Inversely proportional to EOQ (in the denominator). Higher holding cost favors smaller order quantities (lower EOQ) to reduce inventory levels.
Total Inventory Cost	Sum of total ordering cost and total holding cost.	EOQ minimizes this total cost.

Additional Information: Assumptions of the Basic EOQ Model

It's important to understand the assumptions behind the basic EOQ model used here. These include:

Demand is known, constant, and spread evenly throughout the year.
Lead time (the time between placing an order and receiving it) is known and constant.
The price per unit is constant and does not depend on the order quantity (no quantity discounts).
Ordering cost is constant for each order.
Holding cost per unit per year is constant.
Inventory is received in a single delivery.
There are no stockouts or shortages.

While these assumptions might not perfectly reflect real-world scenarios, the basic EOQ model provides a useful starting point for inventory decisions and can often be adapted for more complex situations.

Prepp Team · Answer

1500 units

Prepp Team · Answer

6000 units

Prepp Team · Answer

4500 units

List I (Type of Costing)		List II (Description)
A.	Marginal Costing	I.	Integrated approach to determine product features, product price, product costs and product design that helps ensure a company to earn reasonable profit on new products.
B.	ABC Costing	II.	The amount of any given volume of output by which the aggregate costs are changed if the volume of output is increased by one unit.
C.	Target Costing	III.	Used when identical units are produced through an on-going series of production steps.
D.	Process Costing	IV.	Costing system in which costs being with tracing of activities and then to producing the product.