Economic Ordering Quantity (EOQ). The Gentry Garden Center sells 100,000 bags of lawn fertilizer annually. The optimal safety stock (which is on hand initially) is 1,500 bags. Each bag costs the firm $2.00, inventory carrying costs are 15%, and the cost of placing an order with its supplier is $15. (4 pts) What is the EOQ? What is the maximum inventory of fertilizer? What will be the firm's average inventory? How often must the company order?

1. Annual demand (D) = 100,000 bags

Ordering cost per order (Co) = $15

Holding cost per item per annum (H) = 15% x $2 = $0.30

EOQ = √2DCo

H

EOQ = √2 x 100,000 x $15

0.30

EOQ = 3,162 units

2. Maximum inventory

= Safety stock + EOQ

= 1,500 + 3,162

= 4,662 units

3. Average inventory

= EOQ/2

= 3,162

2

= 1,581 units

4. Number of order

= Annual demand

EOQ

= 100,000

3,162

= 32 times

Explanation:

EOQ is the square root of 2 multiplied by annual demand and ordering cost per order divided by holding cost per item per annum.

Maximum inventory is the aggregate of safety stock and EOQ.

Average inventory is economic order quantity divided by 2

Number of order is the ratio of annual demand to economic order quantity.