Wang Distributors has an annual demand for an airport metal detector of 1,360 un
ID: 384006 • Letter: W
Question
Wang Distributors has an annual demand for an airport metal detector of 1,360 units. The cost of a typical detector to Wang is $400. Carrying cost is estimated to be 19% of the unit cost, and the ordering cost is $27 per order. If Ping Wang, the owner, orders in quantities of 300 or more, he can get a 33% discount on the cost of the detectors. Should Wang take the quantity discount?
What is the EOQ without the discount?
EOQ = ______ units (round your response to one decimal place).
Since the total cost with the discount is (greater than/less than) the total cost without the discount, Wang (should/should not) order 300 units at a time in order to qualify for the discount.
Explanation / Answer
Annual demand = D = 1360 units
Annual unit inventory carrying cost = Ch = 19% of $400 = $76
Ordering cost = Co = $27 / order
Therefore, Economic order quantity ( EOQ )
= Square root ( 2 x Co x D/Ch)
= Square root ( 2 x 27 x 1360 / 76 )
= 31.08 ( 31 rounded to nearest whole number )
ECONOMIC ORDER QUANTITY = 31 DETECTORS
At a price of $400/ unit , annual purchase cost = $400x 1360 = $544000
Annual unit inventory carrying cost = 19% of $400 = $76
Thus total annual inventory carrying cost
= Annual unit inventory carrying cost x Average inventory
=Annual inventory carrying cost x Order quantity /2
= $76 x 31/2
= $1178
Annual ordering cost
= Ordering cost x Number of orders
= $27 x Annual demand /EOQ
= $27 x 1360/31
=$ 1184.51
Thus total cost without discount = $544,000 + $1178 + $1184.51 = $546362.51
For Order quantity = 300 :
Unit price ( with 33% discount) = 67 % of $ 400 = $ 268
Annual demand = 1360 units
Therefore, annual purchase cost of detectors = 1360 x 268 = $ 364480
Annual unit inventory carrying cost = 19% of $268 = $50.92
Thus total annual inventory carrying cost
= Annual unit inventory carrying cost x Average inventory
=Annual inventory carrying cost x Order quantity /2
= $50.92 / unit x 300/2 units = $7638
Ordering cost $ 27/ order
Therefore,
Annual ordering cost
=( Ordering cost / order) x Number of orders
= Ordering cost/order x Annual demand / Order quantity of 300
= $27 x 1360/300
= $122.4
Thus. Total cost with discount = $364480 + $7638 + $122.40 = $372240.40
Since total cost ( $ 372240.40) with discount < Total cost ( $546362.51 ) without discount, Wang should order 300 units at a time in order to qualify for discounts
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