R C Barker Makes Purchasing Decisions For His Company

R C Barker Makes Purchasing Decisions For His Company One Produc

R. C. Barker makes purchasing decisions for his company. One product that he buys costs $50 per unit when the order quantity is less than 500. When the quantity ordered is 500 or more, the price per unit drops to $48. The ordering cost is $30 per order and the annual demand is 7,500 units. The holding cost is 10 percent of the purchase cost. If R. C. wishes to minimize his total annual inventory costs, he must evaluate the total cost for two possible ordering scenarios. What is the optimal order quantity for each scenario? (Round answer to nearest unit.) 200 and 500 None of the above

Sample Paper For Above instruction

The decision-making process regarding order quantities is integral to inventory management and directly impacts a company's operational efficiency and cost minimization strategies. For R. C. Barker, the challenge lies in determining the most cost-effective order quantity under the given pricing and demand conditions. This paper aims to analyze the two scenarios—ordering less than 500 units and ordering 500 or more units—to identify the optimal order quantities that minimize total annual inventory costs.

The core of inventory cost management involves understanding the Economic Order Quantity (EOQ) model, which balances ordering and holding costs to find the most economical order size. The EOQ formula is expressed as:

\[ EOQ = \sqrt{\frac{2DS}{H}} \]

where:

- D = annual demand,

- S = ordering cost,

- H = holding cost per unit per year.

Given the parameters:

- D = 7,500 units,

- S = $30 per order,

- Holding cost rate = 10% of the purchase cost.

When the order quantity is less than 500 units, the unit cost is $50; when 500 or more, the unit cost drops to $48.

Calculating the EOQ for both unit costs provides clarity on the most economical order quantities:

1. For a unit cost of $50:

\[ H = 0.10 \times 50 = \$5 \]

\[ EOQ = \sqrt{\frac{2 \times 7,500 \times 30}{5}} \approx \sqrt{\frac{450,000}{5}} \approx \sqrt{90,000} \approx 300 \text{ units} \]

2. For a unit cost of $48:

\[ H = 0.10 \times 48 = \$4.80 \]

\[ EOQ = \sqrt{\frac{2 \times 7,500 \times 30}{4.80}} \approx \sqrt{\frac{450,000}{4.80}} \approx \sqrt{93,750} \approx 306 \text{ units} \]

Since the EOQ in both cases is less than 500 units, ordering approximately 300 units each time minimizes costs in the first scenario. However, considering the price drop at 500 units, it is cost-effective to evaluate the total annual costs at these specific order quantities.

Total cost (TC) comprises:

\[ TC = DC + \text{Ordering Cost} + \text{Holding Cost} \]

where:

- \( D \times C \) is the purchase cost,

- \(\frac{D}{Q} \times S \) is the total ordering cost,

- \(\frac{Q}{2} \times H \) is the total holding cost.

Calculations:

- For 200 units:

- Purchase cost: \(7,500 \times 50 = \$375,000\)

- Orders per year: \(7,500/200 = 37.5\)

- Ordering costs: \(37.5 \times 30 = \$1,125\)

- Holding costs: \(\frac{200}{2} \times 5 = 100 \times 5 = \$500\)

- Total costs: \$375,000 + \$1,125 + \$500 = \$376,625

- For 500 units:

- Purchase cost: \(7,500 \times 48 = \$360,000\)

- Orders per year: \(7,500/500 = 15\)

- Ordering costs: \(15 \times 30 = \$450\)

- Holding costs: \(\frac{500}{2} \times 4.80 = 250 \times 4.80 = \$1,200\)

- Total costs: \$360,000 + \$450 + \$1,200 = \$361,650

The total annual cost for ordering 500 units is lower than the cost for 200 units, indicating that ordering 500 units strikes a better balance, especially considering the price break. The EOQ calculation supports this, as the EOQ is around 300 units, but the cost structure favors the larger order quantity at 500 units due to lower purchase price and overall minimized total costs. Therefore, the optimal order quantity for the scenario where the order size is 500 or more is exactly 500 units.

In conclusion, R. C. Barker should order 500 units to minimize his total inventory costs, as this scenario offers the lowest total cost considering purchase price, ordering costs, and holding costs. The alternative scenario is less economical because ordering below 500 units incurs higher purchase costs, which outweigh the savings on ordering and holding costs. This analysis underpins the importance of aligning order quantities with cost structures and quantity discounts in inventory management. Moreover, selecting order quantities near the EOQ validates cost efficiency, with the slight difference favoring the larger order size due to discounted unit price and economies of scale.

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