Sarah's Computer City sells 5,000 boxes of CD- RW compact discs per year.She determined that she pays $50 to process an order for discs.Her purchase price is $6 for each box of discs and she has determined that storage costs for one year are 25 percent of the purchase price.Sarah's vendor said that if she purchased 1,000 boxes at a time,she would receive a 10 percent discount.What quantity should Sarah order if the total cost formula is TC = DP +^QIP+^DS?
2 Q

Question

Quizplus · Accepted Answer

To find the optimal quantity to order, we need to use the economic order quantity (EOQ) formula:

EOQ = sqrt((2DP)/S1U1P1)

Where: 
D = annual demand = 5,000
P = purchase price per box = $6
U1 = ordering cost = $50
S1 = storage cost as a percentage of purchase price = 0.25

Plugging in these values:
EOQ = sqrt((2*5,000*50)/(.25*6)) = 577.35, which we can round up to 578.

However, the vendor offers a 10% discount if Sarah orders 1,000 boxes at a time. Since the EOQ is below this threshold, it's best to order in increments of 1,000 to take advantage of the discount. Therefore, Sarah should order 1,000 boxes at a time, for a total of 5 orders per year.

Sarah's Computer City Sells 5,000 Boxes of CD- RW Compact