Outdoor Depot has the opportunity to purchase 1400 lawnmowers a year for its inv
ID: 418937 • Letter: O
Question
Outdoor Depot has the opportunity to purchase 1400 lawnmowers a year for its inventory from a supplier who offers pricing at quantity discounts. The quantities and pricing for each range is shown in the table below. The cost to hold one lawn mower in inventory for one year is 16% of the purchase price. The cost for Outdoor Depot to place an order from this supplier is $110. What is Outdoor Depot's optimal order quantity?
Range
Unit Price
1-499
$300
500-749
$290
750-999
$285
1000-1499
$282
1500 or more
$280
Range
Unit Price
1-499
$300
500-749
$290
750-999
$285
1000-1499
$282
1500 or more
$280
Explanation / Answer
Demand (D) = 1400
Holding % = 16
Holding cost (H) = Price*16%
Ordering cost (S) = 110
EOQ = sqrt(2*D*S/H)
Assuming price of 300, EOQ = sqrt(2*1400*110/(16%*300)) = 80 units
Total cost = D/EOQ*S + EOQ/2*H + Price*D
= 1400/80*110 + 80/2*(30%*300) + 300*1400 = 423,845
Next, assuming EOQ = 500, Price = 290
Total cost = 1400/500*110 + 500/2*(30%*290) + 290*1400 = 417,908
Next, assuming EOQ = 750, Price = 285
Total cost = 1400/750*110 + 750/2*(30%*285) + 285*1400 = 416,305
Next, assuming EOQ = 1000, Price = 282
Total cost = 1400/1000*110 + 1000/2*(30%*282) + 282*1400 = 417,514
Next, assuming EOQ = 1500, Price = 280
Total cost = 1400/1500*110 + 1500/2*(30%*280) + 280*1400 = 425,703
So, minimum cost is for Quantity = 750 at 285$
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