800 units of certain item of stock are needed over each year period. If the unit cost is 400 and the cost of each order is 150, the carrying cost is 1.5%. Then the Economic Order Quantity (EOQ) is:

Concept:

The Economic Order Quantity (EOQ) is a formula used to determine the optimal order quantity that minimizes the total cost of inventory, including ordering and holding costs.

\( EOQ = \sqrt{\frac{2DS}{H}} \)

Where:

• $D$ = Annual demand (units/year)
• $S$ = Ordering cost per order
• $H$ = Holding or carrying cost per unit per year

Given Data:

• Demand $D$ = 800 units/year
• Ordering cost $S$ = 150
• Carrying cost percentage = 1.5%
• Unit cost = 400

Calculate Carrying Cost per Unit:

\( H = 1.5\% \times 400 = \frac{1.5}{100} \times 400 = 6 \, \text{per unit per year} \)

Substitute into the EOQ Formula:

\( EOQ = \sqrt{\frac{2 \times 800 \times 150}{6}} = \sqrt{\frac{240000}{6}} = \sqrt{40000} = 200 \)

The Economic Order Quantity (EOQ) is 200 units.