Question

Economic order quantity ​(EOQ). Tinnendo, Inc. believes it will sell 4 million​ zen-zens, an electronic​ game, this coming year. Note that this figure is for annual sales. The inventory manager plans to order​ zen-zens 36 times over the next year. The carrying cost is ​$0.02 per​ zen-zen per year. The order cost is ​$501 per order. What are the annual carrying​ cost, the annual ordering​ cost, and the optimal order quantity for the​ zen-zens? Verify your answer by calculating the new total inventory cost.

What is the annual carrying cost for the​ zen-zens? $________ ​(Round to the nearest​ dollar.)

What is the annual ordering cost for the​ zen-zens? $_________​(Round to the nearest​ dollar.)

What is the optimal order quantity for the​ zen-zens? ________ ​zen-zens ​(Round to the nearest whole​ unit.)

At the EOQ​, what is the new total inventory​ cost? $_______​(Round to the nearest​ dollar.)

Answer 1

Annual sale, A = 4,000,000
Carrying cost per zen-zen, C = $0.02
Ordering cost per order, O = $501

Answer 1.

Number of orders per year = 36

Order size = Annual sale / Number of orders per year
Order size = 4,000,000 / 36
Order size = 111,111.11 or 111,111

Carrying cost = Carrying cost per zen-zen * (Order size / 2)
Carrying cost = $0.02 * (111,111 / 2)
Carrying cost = $1,111

The annual carrying cost for the zen-zens is $1,111

Answer 2.

Ordering cost = Ordering cost per order * Number of orders per year
Ordering cost = $501 * 36
Ordering cost = $18,036

The annual ordering cost for the zen-zens is $18,036

Answer 3.

EOQ = (2 * A * O / C)^(1/2)
EOQ = (2 * 4,000,000 * $501 / $0.02)^(1/2)
EOQ = 447,660.59 or 447,661

The optimal order quantity for the zen-zens is 447,661 zen-zens.

Answer 4.

Order size = 447,661

Number of orders per year = Annual sale / Order size
Number of orders per year = 4,000,000 / 447,661
Number of orders per year = 8.94 or 9 orders

Carrying cost = Carrying cost per zen-zen * (Order size / 2)
Carrying cost = $0.02 * (447,661 / 2)
Carrying cost = $4,477

Ordering cost = Ordering cost per order * Number of orders per year
Ordering cost = $501 * 9
Ordering cost = $4,509

Total inventory cost = Carrying cost + Ordering cost
Total inventory cost = $4,477 + $4,509
Total inventory cost = $8,986

At EOQ, the new total inventory cost will be $8,986