Carter Company orders 250 units at a time,and places 15 orders per year.Total ordering cost is $1,100 and total carrying cost is $1,100.Which of the following statements is true?
A)the economic order quantity (EOQ)is 250
B)the economic order quantity (EOQ)is more than 250
C)the economic order quantity (EOQ)is less than 250
D)total inventory-related cost is lower than it would be at the economic order quantity (EOQ)
E)none of these

Question

Quizplus · Accepted Answer

The economic order quantity (EOQ) formula is √(2DS/H) where D is the annual demand, S is the ordering cost per order, and H is the holding or carrying cost per unit per year. 
Given information: 
D = (250 units/order) x (15 orders/year) = 3750 units/year 
S = $1,100/15 orders = $73.33/order 
H = $1,100/3750 units = $0.2933/unit/year

Applying the EOQ formula: 
√(2x3750x73.33/0.2933) = √(2,191,250) ≈ 1481.6 
Therefore, the EOQ is more than 250. However, since the company orders in multiples of 250 units, the best choice is still to order 250 units at a time. This is confirmed by checking the total cost at the EOQ and at the nearest multiple of 250:

- Total cost at EOQ: 
Ordering cost = 3750/1481.6 x 73.33 = $186.67 
Carrying cost = 1/2 x 1481.6 x 250 x 0.2933 = $108.75 
Total cost = $186.67 + $108.75 = $295.42

- Total cost at 250 units: 
Ordering cost = 15 x 73.33 = $1099.95 
Carrying cost = 1/2 x 250 x 0.2933 x 3750/250 = $138.74 
Total cost = $1099.95 + $138.74 = $1238.69

Therefore, the best choice for Carter Company is to continue ordering 250 units at a time.

Carter Company Orders 250 Units at a Time,and Places 15