Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.​ Thomas's fastest-moving inventory item has a demand of 6 comma 100 units per year. The cost of each unit is ​$98​, and the inventory carrying cost is ​$9 per unit per year. The average ordering cost is ​$29 per order. It takes about 5 days for an order to​ arrive, and the demand for 1 week is 122 units.​ (This is a corporate​ operation, and there are 250 working days per​ year). ​a) What is the​ EOQ? 198.27 units ​(round your response to two decimal​ places). ​b) What is the average inventory if the EOQ is​ used? 99.14 units ​(round your response to two decimal​ places). ​c) What is the optimal number of orders per​ year? 30.76 orders ​(round your response to two decimal​ places). ​d) What is the optimal number of days in between any two​ orders? 8.12 days ​(round your response to two decimal​ places). ​e) What is the annual cost of ordering and holding​ inventory? ​$ nothing per year ​(round your response to two decimal​ places).

Answer 1

Answer: SEE EXPLANATION

A. 198.27 UNITS

B. 99.14 UNITS

C. 30.76 ORDERS

D. 8.12 DAYS

E. $1,784.43

Explanation:

Given the following ;

Annual order = 6,100

Carrying cost = $9 per unit per year

Ordering cost = $29

A) EOQ =sqrt[( 2 × Annual order × (ordering cost ÷ carrying cost)]

EOQ = sqrt[2 ×6100 × (29÷9)]

EOQ = sqrt(12200 × 3.22222222)

EOQ = 198.27 units

B.) AVERAGE INVENTORY :

EOQ ÷ 2

198.27 ÷ 2 = 99.14 UNITS

C.) Optimal number of orders per year:

Demand / order per year

6,100 ÷ 198.27 = 30.76 orders

D.) Optimal number of days between two orders:

Number of working days ÷ optimal number of orders

250 ÷ 30.76 = 8.12 days.

E.) Annual cost of ordering and holding inventory:

$198.27 × $9 = $1,784.43