Show all work and answer all the questions. The following inventory data have be
ID: 392986 • Letter: S
Question
Show all work and answer all the questions.
The following inventory data have been established for the Thompson Company: .Orders must be placed in multiples of 100 units. Annual sales are 338,000 units. The purchase price per unit is $6. Carrying cost is 20 percent of the purchase price of goods. Fixed order cost is $48. . Three days are required for delivery To avoid shortages, the company will maintain safety stocks equal to 2 days usage (sales) A) What is EOQ? B) How many orders should Thompson place each year? C) What is the expected average inventory, assuming the company will maintain a safety stock of 2 days usage (sales) D) At what inventory level should an order be made? E) Calculate the total cost of ordering and carrying inventories if the order quantity is: 1) 4,000 units; 2) 4,800 units; 3) 3,600 units 4) the EOQ amountExplanation / Answer
Given are following details :
Annualsales = D = 338,000 units
Fixed ordering cost = Co = $48
Annual unit inventory carrying cost = Ch = 20% of purchase price = 0.20 x $6 = $1.2
Therefore,
EOQ = square root ( 2 x Co X D/ Ch) = square root ( 2 x 48 x 338,000/1.2) = 5200 units
The order should be places in multiples of 100 units and 5200 units is multiple of 100 . Therefore, EOQ = 5200 units
EOQ = 5200 UNITS
= Annual sales/ EOQ
= 338,000/5200
= 65 orders
Number of orders should Thompson place every year = 65 orders
Since safety stock requirement is for 2 days,
Safety stock quantity = Annualsales/ 365 days x2 days = 338000/365 x 2 =1852.05 ( 1852 units rounded to nearest whole number )
Expected average Inventory
= EOQ/2 + Safety stock
= 5200/2+ 1852
= 2600 + 1852
= 4452
Expected average inventory = 4452 units
Reorder point
= Average daily sales x Lead time of delivery + Safety stock
= ( 338,000/365) x 3 + 1852
= 2778.08 + 1852
= 4630.08 ( 4630 rounded to nearest whole number )
Order should be made at inventory level of 4630 units
Annual ordering cost = Ordering cost per order x Number of orders = Co x Annual sales/ Order quantity = Co x D / Order quantity = 48x338,000/order quantity = 16224,000/ Order quantity
Annual inventory carrying cost
= Annual unit inventory carrying cost x Average inventory
= Ch x ( Order quantity + safety stock )/2
= $1.2 x ( order quantity + 1852)/2
= $0.6 x Order quantity + $1111.20
Therefore , total cost of ordering and carrying inventory , $
= Co x D/Order quantity + 0.6 x Order quantity + 1111.20
= 16224,000/Order quantity + 0.6 x Order quantity + 1111.20
Based on above equation:
Total cost of ordering and carrying inventory for order quantity of 4,000 units = $7567.20
Total cost of ordering and carrying inventory for order quantity of 4800 units = $7371.20
Total cost of ordering and carrying inventory for order quantity of 3600 units = $7777.87
Total cost of ordering and carrying inventory for order quantity of EOQ = $7351.20
EOQ = 5200 UNITS