Given the following data for particular inventory item:

your usage of a given inventory is 500 units per week. the ordering cost is $40 per order and the carrying cost are one cent per unit each week. it takes three weeks to receive an order, and the price of the item itself is 50 cents per unit.

1. what is the economic order quantity for this item?

2. what is the reorder point?

3. what is average inventory level?

4. what are the average weekly ordering cost?

5. what are the weekly carrying cost?

6. what are average weekly total cost excluding the cost of the inventory item?

7. what are average weekly total cost including the cost of the inventory item?

8. what is the reorder point if safety stock is kept at 250 units?

1.The economic order quantity for this item is 2000 units.

2.The reorder point is 1500 units.

3. Average inventory level is 1250 units.

4.The average weekly ordering cost is $13.33.

5.The weekly carrying cost is $5.

6.The average weekly total cost excluding the cost of the inventory item is $18.33.

7.The average weekly total cost including the cost of the inventory item is $268.33.

8. The reorder point if safety stock is kept at 250 units is 1750 units.

Explanation:

1.The economic order quantity (EOQ) for this item can be computed using the following formula:

EOQ=√[(2 × Demand × Ordering costs) ÷ Carrying costs]

EOQ=√[(2 × 500 × 40) ÷ 0.01]

EOQ=√4,000,000 = 2,000 units.

2.The reorder point can be computed using the following formula:

Reorder point= Average lead time × Average units usage

Reorder point= 3 × 500.

Reorder point= 1,500 units.

3. The average inventory level can be computed using the following formula;

The average inventory level = (Beginning Inventory + Ending Inventory)/2.

The average inventory level = (2,000 + 500)/2.

The average inventory level = 1250 units.

4.The average weekly ordering cost can be computed using the following formula:

The average weekly ordering cost = Ordering cost per order/order lead time

The average weekly ordering cost = 40/3

The average weekly ordering cost = $13.33.

5.The weekly carrying cost can be computed using the following formula:

The weekly carrying cost = Carrying cost per unit × Inventory for the week.

The weekly carrying cost = 0.01 × 500.

The weekly carrying cost = $5.

6.The average weekly total cost excluding the cost of the inventory item can be computed using the following formula:

Relevant cost to be considered is ordering cost and carrying costs.

The average weekly total cost excluding the cost of the inventory item = weekly Ordering costs + weekly Carrying costs.

The average weekly total cost excluding the cost of the inventory item = (40 / 30) + (0.01 × 500)

The average weekly total cost excluding the cost of the inventory item = 13.33 + 5.

The average weekly total cost excluding the cost of the inventory item = $18.33.

7.The average weekly total cost including the cost of the inventory item can be computed using the following formula:

The average weekly total cost including the cost of the inventory item = Weekly ordering cost + Weekly carrying costs + Weekly inventory cost

NB: The weekly inventory costs can be obtained by multiplying the unit price by the number of units demanded every week.

The average weekly total cost including the cost of the inventory item = (40/3) + (0.01 × 500) + (0.50 × 500)

The average weekly total cost including the cost of the inventory item = 13.33 + 5 + 250

The average weekly total cost including the cost of the inventory item = $268.33.

8. The reorder point if safety stock is kept at 250 units can be computed using the following formula:

The reorder point inclusive of a safety stock = (Average sale × lead time) + Safety stock

The reorder point inclusive of a safety stock = (500 × 3) + 250

The reorder point inclusive of a safety stock = 1500 + 250

The reorder point inclusive of a safety stock = 1750 units.

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