manufacturing firm uses a particular component, which it orders from a supplier. The supplier has provided the following discounted pricing for the component. Number of components ordered Discount per unit1-199 $65200-599 $59600+ $56The manufacturing company uses 700 of the components annually. The annual carrying cost is $14 per unit, the ordering cost is $275. Determine the amount the firm should order. (answer should be in whole number)
Question
manufacturing firm uses a particular component, which it orders from a supplier. The supplier has provided the following discounted pricing for the component. Number of components ordered Discount per unit1-199 59600+ 14 per unit, the ordering cost is $275. Determine the amount the firm should order. (answer should be in whole number)
Solution
To determine the amount the firm should order, we can use the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of ordering and holding inventory. It is given by the formula:
EOQ = sqrt((2DS)/H)
where: D = Demand rate for the year S = Order cost per order H = Holding or carrying cost per unit per year
Given: D = 700 units (annual demand) S = 14 (carrying cost)
Substituting these values into the EOQ formula, we get:
EOQ = sqrt((2700275)/14) = 158.11 units
Since we can't order a fraction of a unit, we'll round this up to the nearest whole number, which is 159 units.
However, given the supplier's discount structure, it would be more cost-effective to order in larger quantities. If the firm orders 200-599 units, the cost per unit drops to 56.
Therefore, despite the EOQ suggesting 159 units, it would be more cost-effective for the firm to order 600 units at a time to take advantage of the supplier's volume discount.
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