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A local food processing firm uses (demand) 24,000 glass jars to produce gourmet jams and jellies per year. It costs the firm $60 each time it places an order for jars with the manufacturers. The inventory holding cost is $0.8 per jar per year. The stock is received 4 working days after an order has been placed. No backorders are allowed. Because of space limitations, suppose the firm orders 300 jars at a time. What would be the annual cost saved by shifting from the 300-jars order policy to the EOQ?

User Hoshouns
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Final answer:

By shifting from the 300-jars order policy to the Economic Order Quantity (EOQ) model, the local food processing firm can save approximately $2,742.60 per year. This cost saving is achieved by optimizing the order quantity to minimize the total cost of ordering and holding inventory.

Step-by-step explanation:

The local food processing firm currently uses a 300-jars order policy to purchase glass jars, but wants to know the annual cost saved by shifting to the Economic Order Quantity (EOQ) model. In the EOQ model, the firm determines the optimal order quantity that minimizes the total cost of ordering and holding inventory. To calculate the annual cost savings, we need to compare the costs under the current 300-jars order policy and the EOQ model.

Under the 300-jars order policy, the firm places an order for 300 jars. The number of orders placed per year can be calculated as total demand divided by the number of jars ordered per order: 24,000 jars / 300 jars = 80 orders per year. The annual ordering cost can then be calculated as the number of orders multiplied by the ordering cost per order: 80 orders * $60/order = $4,800.

The annual holding cost can be calculated as the average inventory multiplied by the holding cost per jar: 300 jars / 2 (since we assume equal demand throughout the year) * $0.8/jar = $120.

Therefore, the total annual cost under the 300-jars order policy is $4,800 (ordering cost) + $120 (holding cost) = $4,920.

Now, let's calculate the EOQ. The EOQ formula is given by:

EOQ = sqrt((2 * demand * ordering cost) / holding cost) = sqrt((2 * 24,000 * $60) / $0.8) = sqrt(36,480,000) = 6,040 jars (rounded to the nearest whole number).

The number of orders per year under the EOQ model can be calculated as total demand divided by the EOQ: 24,000 jars / 6,040 jars = 3.97 orders per year (rounded to the nearest whole number).

The annual ordering cost under the EOQ model can then be calculated as the number of orders multiplied by the ordering cost per order: 3.97 orders * $60/order = $238.20 (rounded to the nearest cent).

The annual holding cost under the EOQ model can be calculated as the average inventory multiplied by the holding cost per jar: 6,040 jars / 2 (since we assume equal demand throughout the year) * $0.8/jar = $1,939.20 (rounded to the nearest cent).

Therefore, the total annual cost under the EOQ model is $238.20 (ordering cost) + $1,939.20 (holding cost) = $2,177.40 (rounded to the nearest cent).

The annual cost savings by shifting from the 300-jars order policy to the EOQ model can be calculated as the difference between the total annual costs under the two policies: $4,920 (300-jars order policy) - $2,177.40 (EOQ model) = $2,742.60 (rounded to the nearest cent).

User Harry Ng
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