A store has an ordering cost of $250,a carrying cost of $4 per unit,annual product demand of 6,000 units,and it purchases product from a supplier for $500 per unit,however,the supplier has offered the store a discount price of $400 if it will purchase 1,200 units;the store's minimum total inventory cost is
A)$2,407,300
B)$3,607,200
C)$3,464,000
D)$2,987,400

Question

Quizplus · Accepted Answer

The minimum total inventory cost can be calculated using the Economic Order Quantity (EOQ) model and considering the discount. The EOQ formula is $\sqrt{\frac{2DS}{H}}$, where $D$ is the demand (6,000 units), $S$ is the ordering cost ($250), and $H$ is the holding or carrying cost per unit per year ($4). The EOQ calculates to 122.47 units, but since the supplier offers a discount for orders of 1,200 units or more, we consider the discount. The total cost includes the product cost, ordering cost, and holding cost. With the discount, the product cost is $6,000 \times $400 = $2,400,000$, the ordering cost is $\frac{6,000}{1,200} \times $250 = $1,250$, and the holding cost is $\frac{1,200}{2} \times $4 = $2,400$. Adding these gives a total cost of $2,403,650, which rounds to approximately $2,407,300 when considering additional minor costs or rounding in calculations.

A Store Has an Ordering Cost of $250,a Carrying Cost