This Question: 10 pts 15 of 15 (0 complete) This Quiz: 70 pts possible Thomas Kr
ID: 330531 • Letter: T
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This Question: 10 pts 15 of 15 (0 complete) This Quiz: 70 pts possible 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 6,050 units per year. The cost of each unit is $102, and the inventory carrying cost is $8 per unit per year. The average ordering cost is $29 per order. It takes about 5 days for an order to amive, and the demand for 1 week is 121 units. (This is a corporate operation, and there are 250 working days per year) a) What is the EOQ? units (round your response to two decimal places). b) What is the average inventory if the EOQ is used? units round your response to two decimal places. What is the optimal number of orders per year? orders (round your response to two decimal places) d) What is the optimal number of days in between any two orders? ? days ound your esponse to two decimal places e) What is the annual cost of ordering and holding inventory? S ? per year round your response to two e malgaces f What is the total annual inventory cost, including the cost of the 6,050 units? S per year (round your response to two decimal places)Explanation / Answer
Given are the following details :
Annual demand = D = 6050 units
Annual ordering cost = Co =$29 per order
Inventory carrying cost = Ch = $8 per unit per year
Economic Order Quantity ( EOQ )
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 29 x 6050/ 8 )
=209.43 ( 209 rounded to nearest whole number )
EOQ = 209
Average inventory = EOQ / 2 = 209/2 = 104.5
Optimal number of orders per year = Annual demand / EOQ = 6050/ 209 = 28.95 ( rounded to 2 decimal places )
Daily demand = 6050/250 = 24.2
Optimal number of days between two orders = EOQ / Daily demand = 209/24.2 = 8.636 ( 8.64 days )
Annual cost of ordering
= Ordering cost x Number of orders
= Ordering cost x Annual demand / EOQ
= $29 x 6050/ 209
= $839.47
Annual holding cost
= Annual unit holding cost x Average inventory
= Ch x EOQ / 2
= $8 x 209/2
= $836
Annual cost of ordering and holding inventory = $839.47 + $836 = $1675.47
Cost of 6050 units = Unit price x Number of units = $102 x 6050 =$617100
Total annual inventory cost including cost of 6050 units = $617100 + $1675.47 = $618775.47
EOQ = 209
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