The Current Order Quantity For Paul’s Pasta Pinwheels Is 200

The Current Order Quantity For Pauls Pasta Pinwheels Is 200 boxes

The Current Order Quantity For Pauls Pasta Pinwheels Is 200 boxes

The current order quantity for Paul’s Pasta Pinwheels is 200 boxes. The order cost is $4 per order, the holding cost is $0.40 per box per year, and the annual demand is 500 boxes per year. A. Calculate the annual holding cost plus the annual ordering cost to get the total annual cost when using an order quantity of 200 boxes. B. Calculate the EOQ and the total annual cost for this order. 3. Hottenstein, Griffith, and Hult, attorneys at law, do a great deal of printing. The firm uses a single type of printer with annual demand for print cartridges of 480 per year. The order cost is $15 per order, and carrying cost of $35 per cartridge. a. How many print cartridges should the firm order at one time? b. What is the time between orders?

Paper For Above instruction

Inventory management is vital for businesses to minimize costs associated with ordering and holding inventory. In this paper, we analyze two scenarios involving economic order quantity (EOQ) models to determine optimal order quantities and associated costs for a food manufacturing company and a law firm.

Scenario 1: Paul’s Pasta Pinwheels Inventory Cost Analysis

Paul’s Pasta Pinwheels currently orders 200 boxes per cycle, with an order cost of $4, a holding cost of $0.40 per box annually, and an annual demand of 500 boxes. To analyze the efficiency of this order quantity, we compute the total annual cost, which comprises ordering costs and holding costs. The total annual cost for a given order quantity is the sum of annual ordering costs and annual holding costs.

Annual ordering cost is calculated as:

Order Cost per Order × Number of Orders per Year = $4 × (Annual Demand / Order Quantity)

Annual holding cost is:

Holding Cost per Unit × Average Inventory = $0.40 × (Order Quantity / 2)

Applying these formulas for the current order quantity of 200 boxes:

  • Number of orders per year = 500 / 200 = 2.5 orders
  • Annual ordering cost = $4 × 2.5 = $10
  • Average inventory = 200 / 2 = 100 boxes
  • Annual holding cost = $0.40 × 100 = $40
  • Total annual cost = Ordering cost + Holding cost = $10 + $40 = $50

This analysis shows that, with the current ordering strategy, the total annual inventory-related costs amount to $50.

Next, we calculate the EOQ to identify the optimal order quantity that minimizes total costs. The EOQ formula is:

EOQ = sqrt((2 × Demand × Ordering Cost) / Holding Cost)

Substituting the given values:

EOQ = sqrt((2 × 500 × 4) / 0.40) = sqrt((4000) / 0.40) = sqrt(10000) = 100 boxes

The EOQ is therefore 100 boxes. To find the total annual cost at this EOQ:

  • Number of orders = 500 / 100 = 5
  • Annual ordering cost = $4 × 5 = $20
  • Average inventory = 100 / 2 = 50 boxes
  • Annual holding cost = $0.40 × 50 = $20
  • Total annual cost = $20 + $20 = $40

The EOQ reduces the total inventory costs from $50 to $40, indicating a more cost-efficient order quantity than the current 200 boxes.

Scenario 2: Printing Supplies Inventory Cost Management for Law Firm

The law firm’s annual demand for print cartridges is 480 units, with an order cost of $15 per order and a carrying cost of $35 per cartridge annually. To determine the optimal order quantity, we again use the EOQ model:

EOQ = sqrt((2 × Demand × Order Cost) / Carrying Cost)

Plugging in the values:

EOQ = sqrt((2 × 480 × 15) / 35) = sqrt((14,400) / 35) ≈ sqrt(411.43) ≈ 20.28

Since order quantities are typically whole numbers, the firm should order approximately 20 cartridges per order to minimize costs.

To determine the interval between orders, we calculate the cycle time:

Cycle Time = (Number of working days in a year) / (Number of orders per year)

The number of orders per year at EOQ is:

Number of Orders = Demand / EOQ = 480 / 20 = 24 orders

Assuming an approximate 250 working days in a year, the time between orders is:

Time Between Orders = 250 / 24 ≈ 10.42 days

This indicates the law firm should reorder approximately every 10 to 11 days to maintain optimal inventory levels.

These calculations reinforce the importance of applying EOQ models to inventory management, as they help identify cost-efficient order quantities and reorder intervals that reduce unnecessary expenses and improve operational efficiency.

Conclusion

Proper inventory management using EOQ calculations allows organizations like food producers and service providers to streamline their ordering processes, minimize costs, and avoid shortages or excess inventory. The analysis demonstrates that frequently used formulas can effectively reduce costs when correctly applied, ensuring businesses remain competitive and financially optimized.

References

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