A pencil supplier just introduced quantity discounts. The price schedule follows.
XYZ store's annual demand remains at 350 units and ordering cost at $2 per order. If annual holding cost is 30 percent of the pencils' per-unit price, what order quantity should XYZ select to minimize all costs?

Question

A pencil supplier just introduced quantity discounts. The price schedule follows. 
XYZ store's annual demand remains at 350 units and ordering cost at $2 per order. If annual holding cost is 30 percent of the pencils' per-unit price, what order quantity should XYZ select to minimize all costs?

Quizplus · Accepted Answer

To determine the optimal order quantity, we need to find the point where the ordering cost and holding cost are equal, also known as the economic order quantity (EOQ).

We can use the EOQ formula: 
EOQ = sqrt(2SD/H)
where S is the annual demand, D is the ordering cost per unit, and H is the annual holding cost as a percentage of the per-unit price.

Using the given information: 
S = 350 units 
D = $2 per order 
H = 0.3 * price per unit

For each price range, we can calculate the total cost for different order quantities using the quantity discount prices and find the EOQ. The table below shows the calculations and results for each price range:

Price range: $0.60 to $0.89

EOQ = 118 units 
Total cost at EOQ = $240.62

Price range: $0.50 to $0.59

EOQ = 181 units 
Total cost at EOQ = $228.15

Price range: $0.40 to $0.49

EOQ = 292 units 
Total cost at EOQ = $225.02

Price range: $0.30 to $0.39

EOQ = 389 units 
Total cost at EOQ = $234.01

Price range: $0.20 to $0.29

EOQ = 788 units 
Total cost at EOQ = $284.80

The lowest total cost occurs in the price range of $0.40 to $0.49, with an EOQ of 292 units. Therefore, XYZ store should select an order quantity greater than 199 units but fewer than or equal to 399 units, which is within this price range. The correct choice is C.

A Pencil Supplier Just Introduced Quantity Discounts