A particular raw material is available to a company at three different prices, d
ID: 332517 • Letter: A
Question
A particular raw material is available to a company at three different prices, depending on the size of the order Less than 100 pounds 100 pounds to 1,999 pounds 2,000 pounds or more $15 per $14 Per $13 Per pound pound pound The cost to place an order is $60. Annual demand is 2,900 units. Holding (or carrying) cost is 30 percent of the material price What is the economic order quantity to buy each time, and its total cost? (Round your answers to the nearest whole number.) Economic order quantity Total cost poundsExplanation / Answer
The formula for Economic Order Quantity ( EOQ ) is as follows :
EOQ = square root ( 2 x Co x D/ Ch )
Co = Ordering cost = $60
D = Annual demand = 2900 units
Ch = Annual unit holding cost = 30% of material price
Since price varies depending on quantity , Ch will also vary depending on quantity .
Therefore, there will be different values of EOQ for different values of Ch corresponding to relevant quantity slab
The calculations for different EOQ values are presented below :
Quantity slab ( Pounds )
Material price / pound ( $)
Ch value ( $), 30% of Material price/Pound
EOQ ( rounded to nearest whole number0
Less than 100
15
4.5
278
100 to 1999
14
4.2
288
2000 or more
13
3.9
299
Since it is only the EOQ of 288 which falls within its respective quantity slab, it should be the ideal EOQ which minimizes total annual ordering cost and total annual inventory holding cost )
However , we will compare total cost ( i.e. annual purchase cost + annual ordering cost + annual inventory holding cost for following quantities:
Total cost for EOQ = 288 :
Annual purchasing cost = 2900 x $14 = $40600
Annual ordering cost = Ordering cost x Number of orders = Ordering cost x Annual demand/ Order quantity = Co x D/EOQ = $60 x 2900/288 = $604.16
Annual inventory holding cost = Annual unit inventory cost x Average inventory = Ch x EOQ/2 = $4.2 x 288/2 = $604.80
Total cost for EOQ of 288 = $40600 + $604.16 + $604.80 = $41808.96
Total cost for order quantity of 2000 :
Annual purchasing cost = 2900 x $13 = $37700
Annual ordering cost = Ordering cost x Number of orders = Ordering cost x Annual demand/ Order quantity = Co x D/order qty = $60 x 2900/200 = $87
Annual inventory holding cost = Annual unit inventory cost x Average inventory = Ch x Order quantity/ 2 = 3.9 x 2000/2 = $3900
Total cost for order quantity of 2000 = $37700 + $87 + $3900 = $41687
Since total cost for order size of 2000 < Total cost for order size 288 , Economic order quantity will be 2000 pounds
ECONOMIC ORDER QUANTITY = 2000
TOTAL COST = $41687
Quantity slab ( Pounds )
Material price / pound ( $)
Ch value ( $), 30% of Material price/Pound
EOQ ( rounded to nearest whole number0
Less than 100
15
4.5
278
100 to 1999
14
4.2
288
2000 or more
13
3.9
299
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