A large bakery buys flour in 25-pound bags. The bakery uses an average of 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $4 per order. Annual carrying cost are $30 per bag. Assume that each order comes in one batch.
(a) Determine the economic order quantity.
(b) What is the average inventory level?
(c) How many orders does de company place per year?
(d) Demonstrate that your order quantity in (a) is optimal by showing that annual ordering costs = annual holding costs.

a) EOQ = 36 units

b) Average Inventory=18 units

c) No of orders per year= 135 times

d) Ordering cost ($540 ) = Carrying cost ($540)

Explanation:

The economic order quantity is the order size that minimizes the the balance of holding cost and ordering cost.

It is calculated using the formula below:

a) EOQ = √ 2×Co×D/Ch

Co- 4, Ch- 30 - D - 4, 860

EOQ =  √ 2×4×4,860/30

      = 36 units

b) Average Inventory = EOQ /2

= 36/2 = 18 units

c) No of orders per year = Annual demand/ EOQ

=4,860/36 = 135 times

d) At the EOQ, the holding cost = Ordering cost

Holding cost = holding cost per unit × Average inventory

= $30×  18 = $540

Annual ordering cost = ordering cost per unit × No of orders

= $4 × 135 = $540

Ordering cost ($540 ) = Carrying cost ($540)