Calculate EOQ and plot a graph with the following information.
Annual Usage= 1600 units
Holding Cost= $8 unit/yr
Ordering Cost = $100 unit/yr
Price of per Unit= $50
The Correct Answer and Explanation is :
Economic Order Quantity (EOQ) Calculation and Analysis
EOQ Calculation
The Economic Order Quantity (EOQ) is calculated using the formula:
[
EOQ = \sqrt{\frac{2DS}{H}}
]
where:
- ( D = 1600 ) units/year (Annual Demand),
- ( S = 100 ) per order (Ordering Cost),
- ( H = 8 ) per unit/year (Holding Cost).
[
EOQ = \sqrt{\frac{2 \times 1600 \times 100}{8}} = \sqrt{40000} = 200 \text{ units}
]
Thus, the EOQ is 200 units, meaning that ordering 200 units at a time minimizes the total inventory cost.
Graph Explanation
The graph displays the relationship between different order quantities and their corresponding total costs. The total cost consists of:
- Ordering Cost: Decreases as the order size increases since fewer orders are placed per year.
- Holding Cost: Increases with order size since more inventory is held at any given time.
- Total Cost: The sum of holding and ordering costs. The EOQ point (200 units) is marked, where total cost is minimized.
From the plotted graph, you can observe that ordering quantities much lower or much higher than 200 units results in higher costs, confirming EOQ as the optimal order quantity.