Calculating EOQ (Economic Order Quantity)

1. Understanding the Variables:

- Ordering Cost: The cost incurred to place an order for inventory. In this case, it is 200.
- Quarterly Consumption: The amount of inventory used or sold in a quarter. In this case, it is 3000 units.
- Carrying Cost: The cost of holding inventory. It is calculated as a percentage of the average inventory. In this case, it is 12% of the average inventory.

2. Formula for EOQ:

The Economic Order Quantity (EOQ) can be calculated using the following formula:

EOQ = √((2 * Ordering Cost * Quarterly Consumption) / Carrying Cost)

3. Calculating Average Inventory:

To calculate the average inventory, we divide the EOQ by 2. This is because the inventory level fluctuates between 0 and EOQ throughout the ordering cycle.

Average Inventory = EOQ / 2

4. Calculating Carrying Cost:

Carrying Cost is calculated as a percentage of the average inventory. In this case, it is 12% of the average inventory.

Carrying Cost = 12% * Average Inventory

5. Plugging in the Values:

Now, let's plug in the given values into the formula to calculate EOQ:

EOQ = √((2 * 200 * 3000) / (0.12 * Average Inventory))

6. Solving for EOQ:

To solve for EOQ, we need to calculate the Average Inventory. Let's assume an initial guess for EOQ, calculate the Average Inventory, and then refine the EOQ based on the calculated Average Inventory.

- Initial Guess for EOQ: Let's assume an initial EOQ of 1000 units.
- Average Inventory: Average Inventory = EOQ / 2 = 1000 / 2 = 500 units
- Carrying Cost: Carrying Cost = 12% * Average Inventory = 0.12 * 500 = 60

Now, let's plug in the values into the EOQ formula and solve for EOQ:

EOQ = √((2 * 200 * 3000) / 60) = √(12000000 / 60) = √200000 = 447.21 (rounded to two decimal places)

7. Refining the EOQ:

Since the initial guess of 1000 units resulted in an EOQ of 447.21, we need to refine our guess. Let's try a higher EOQ:

- New Guess for EOQ: Let's assume a new EOQ of 500 units.
- Average Inventory: Average Inventory = EOQ / 2 = 500 / 2 = 250 units
- Carrying Cost: Carrying Cost = 12% * Average Inventory = 0.12 * 250 = 30

Now, let's plug in the values into the EOQ formula and solve for EOQ:

EOQ = √((2 * 200 * 3000) / 30) = √(12000000 / 30) = √400000 = 632.46 (rounded to two decimal places)

8. Final EOQ:

After refining the guess,