Explanation:
The Economic Order Quantity (EOQ) is an inventory control model that determines the optimal quantity of goods to order in order to minimize inventory carrying costs and ordering costs. It is based on the trade-off between holding inventory and ordering inventory.

Optimum lot size:
The Economic Order Quantity (EOQ) is often referred to as the optimum lot size because it represents the quantity of goods that minimizes the total cost of inventory. It is the point at which the carrying costs and ordering costs are balanced, resulting in the lowest total cost.

Carrying costs:
Carrying costs refer to the costs associated with holding inventory, such as storage costs, insurance, obsolescence, and the opportunity cost of tying up capital in inventory. These costs increase as the level of inventory increases.

Ordering costs:
Ordering costs refer to the costs associated with placing and receiving an order, such as the cost of transportation, paperwork, and processing. These costs decrease as the lot size increases because fewer orders need to be placed.

Trade-off:
The EOQ model takes into account the trade-off between carrying costs and ordering costs. If the lot size is too small, ordering costs will be high due to frequent orders, but carrying costs will be low. On the other hand, if the lot size is too large, ordering costs will be low, but carrying costs will be high.

Formula:
The EOQ formula is derived by balancing the carrying costs and ordering costs. The formula is as follows:

EOQ = √((2 * D * S)/H)

Where:
EOQ = Economic Order Quantity
D = Annual demand (in units)
S = Ordering cost per order
H = Holding cost per unit per year

Benefits of EOQ:
- Minimizes inventory carrying costs by reducing the amount of inventory held.
- Minimizes ordering costs by optimizing the order quantity.
- Helps in maintaining an optimum balance between holding inventory and placing orders.
- Reduces the risk of stockouts and excess inventory.

Conclusion:
The Economic Order Quantity (EOQ) is the optimum lot size that minimizes the total cost of inventory by balancing carrying costs and ordering costs. It helps in determining the optimal quantity of goods to order and maintaining an optimal inventory level.