**EOQ Model**:
The Economic Order Quantity (EOQ) model is a mathematical model used to determine the optimal order quantity that minimizes the total cost of inventory management. It takes into account the trade-off between ordering costs and carrying costs.

**Unit Ordering Cost**:
The unit ordering cost represents the cost associated with placing an order, such as paperwork, transportation, and processing fees. It is typically assumed to be constant regardless of the order quantity.

**Explanation**:
When the unit ordering cost is doubled, it affects the EOQ in the following way:

- **Inverse Relationship**: The EOQ and the unit ordering cost have an inverse relationship. This means that as the unit ordering cost increases, the EOQ decreases, and vice versa.

- **Mathematical Relationship**: The relationship between the unit ordering cost (C) and the EOQ (Q) is expressed mathematically as follows:

EOQ = sqrt((2 * D * S) / C)

Where:
- D = Annual demand (number of units)
- S = Cost per order (ordering cost)
- C = Carrying cost per unit per year

- **Doubling the Unit Ordering Cost**: When the unit ordering cost is doubled, it means that the value of C in the EOQ formula is doubled.

- **Effect on EOQ**: To understand the effect of doubling the unit ordering cost on the EOQ, we can analyze the EOQ formula.

EOQ = sqrt((2 * D * S) / C)

When the unit ordering cost (C) is doubled, it becomes 2C.

EOQ = sqrt((2 * D * S) / 2C)

Simplifying the equation:

EOQ = sqrt((D * S) / C)

As we can see, the EOQ is equal to the square root of the original EOQ when the unit ordering cost is doubled.

- **Approximate Increase**: The square root of 2 is approximately 1.414. Therefore, when the unit ordering cost is doubled, the EOQ increases by approximately 1.414 times.

Therefore, the correct answer is option 'C': The EOQ increases 1.414 times when the unit ordering cost is doubled.