**When quantity discounts are allowed, the cost-minimizing order quantity**

** ****Options:**

A. is always an EOQ quantity. B. minimizes the sum of holding and ordering costs. C. minimizes the unit purchase price. D. may be a quantity below that at which one qualifies for that price. E. minimizes the sum of holding, ordering, and product costs. |

### The Correct Answer Is:

E. minimizes the sum of holding, ordering, and product costs.

**Correct Answer Explanation: E. minimizes the sum of holding, ordering, and product costs.**

When quantity discounts are in play, determining the cost-minimizing order quantity becomes a crucial decision. The correct answer, E, states that this quantity minimizes the sum of holding, ordering, and product costs. Let’s delve into the reasoning behind this:

**i. Minimizing the sum of holding costs:**

Holding costs refer to expenses incurred while holding inventory, including warehousing, insurance, and obsolescence. Ordering excessive quantities can lead to higher holding costs due to the increased time the inventory remains in storage. Conversely, ordering too little might trigger frequent orders, incurring more ordering costs.

**ii. Minimizing ordering costs:**

Ordering costs encompass expenses involved in placing and receiving an order, such as administrative expenses, transportation, and supplier-related charges. Ordering too frequently increases these costs, while infrequent ordering might lead to larger batch costs.

**iii. Minimizing product costs:**

Considering the cost per unit, when quantity discounts are involved, the cost-minimizing order quantity must take into account these discounts. This involves evaluating various price breaks at different quantities to determine the optimal balance between unit purchase price and total cost.

**Now, let’s break down why the other options are not the correct answers:**

**A. Is always an EOQ quantity:**

The Economic Order Quantity (EOQ) is a calculation that determines the optimal order quantity to minimize total inventory costs, assuming no quantity discounts. However, when quantity discounts are available, the optimal order quantity may deviate from the EOQ.

Quantity discounts alter the cost structure by providing price breaks at various order quantities. As a result, the quantity that minimizes costs considering these discounts might differ from the traditional EOQ.

While the EOQ is an essential concept in inventory management, it’s not always synonymous with the cost-minimizing order quantity, especially in scenarios involving quantity discounts that impact unit purchase prices.

**B. Minimizes the sum of holding and ordering costs:**

This option emphasizes the significance of holding and ordering costs, which are crucial components in inventory management.

However, when quantity discounts are involved, the optimal order quantity considers not only holding and ordering costs but also product costs influenced by the price per unit at different quantity levels.

Focusing solely on holding and ordering costs overlooks the potential impact of quantity discounts on unit purchase prices, which can significantly affect the overall total cost.

**C. Minimizes the unit purchase price:**

While considering the unit purchase price is essential, especially when quantity discounts are available, it doesn’t encompass the entirety of costs associated with inventory management.

Opting for the lowest unit purchase price might lead to overlooking the impact of holding and ordering costs on the total cost. For instance, a lower unit price at higher quantities might result in increased holding costs, negating the apparent savings from the cheaper unit price.

**D. May be a quantity below that at which one qualifies for that price:**

This option acknowledges the possibility of ordering below the quantity required to qualify for a discount. However, it doesn’t encompass the comprehensive evaluation of all relevant costs.

While missing out on a quantity discount might be a consideration, the cost-minimizing order quantity involves analyzing the interplay of holding, ordering, and product costs at various quantity levels to optimize total costs.

In summary, when quantity discounts are present, determining the cost-minimizing order quantity entails a holistic assessment that considers holding costs, ordering costs, and product costs influenced by varying unit purchase prices at different quantities.

This comprehensive evaluation aims to minimize the total cost associated with inventory management rather than focusing solely on individual cost components.

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