Final answer:
The optimal order size for the item is approximately 90 units calculated using the EOQ model. The annual cost of ordering the item is approx. $222.20, calculated by multiplying the amount of times an order is placed per year by the order cost.
Step-by-step explanation:
The question pertains to determining the optimal order size for a company's inventory management system and the related costs of ordering. To calculate the optimal order size, the Economic Order Quantity (EOQ) model is typically used, which is designed to minimize the cost of ordering and holding inventory. Typically, EOQ is calculated using the square root of ((2DS)/H), where D is the demand rate, S is the ordering cost per order, and H is the holding cost per unit per time period.
Given that the company uses about 2,000 units of Item X (D), each order costs $10 (S), and the holding cost is $5 per unit (H), the EOQ equation would be:
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- EOQ = √((2*2000*10)/5)
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- EOQ = √((40000)/5)
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- EOQ = √8000
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- EOQ = 89.44
Therefore, the company should order approximately 90 units of Item X each time they place an order to minimize costs.
To calculate the annual cost of ordering Item X, you would divide the annual demand by the EOQ to determine how many orders are placed per year, and then multiply that by the ordering cost. For instance:
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- Number of orders per year = 2000 / 90
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- Number of orders per year = 22.22
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- Annual ordering cost = Number of orders per year * Ordering cost
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- Annual ordering cost = 22.22 * 10
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- Annual ordering cost = $222.20
The annual ordering cost for Item X would therefore be approximately $222.20.