Question

Apply the EOQ model to the following quantity discount situation for which D= 700 units per year, C = $35, and the annual holding cost rate is 20%. (Round your answers to the nearest integer.)

Discount Discount
Category Order Size (%) Unit Cost Order Quantity
1 0 to 99 0 $10.00 Q₁ =
2 100 or more 3 $9.70 Q₂ =

Answer 1

To apply the EOQ model to this quantity discount situation, calculate the EOQ for each discount category and compare the total costs. The EOQ formula is EOQ = √((2DS) / H), where D is the annual demand, S is the cost of placing an order, and H is the annual holding cost rate. For this situation, the more cost-effective option is to order the quantity that falls under Discount Category 2, which is 100 or more units.

Step-by-step explanation:

To apply the EOQ model to this quantity discount situation, we need to calculate the Economic Order Quantity (EOQ) for each discount category and then compare the total costs for each. The EOQ formula is given by:

EOQ = √((2DS) / H), where D is the annual demand, S is the cost of placing an order, and H is the annual holding cost rate.

For Discount Category 1 (0 to 99 units), the unit cost is $10.00 and for Discount Category 2 (100 or more units), the unit cost is $9.70. Let's calculate the EOQ for each category:

EOQ for Category 1 = √((2 x 700 x 10) / (0.20)) = 74 units (rounded to the nearest integer)

EOQ for Category 2 = √((2 x 700 x 9.70) / (0.20)) = 73 units (rounded to the nearest integer)

Therefore, for this quantity discount situation, it is more cost-effective to order the quantity that falls under Discount Category 2, which is 100 or more units.