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 minimize all costs, we need to find the optimal order quantity that minimizes the sum of ordering cost and holding cost.

Using the quantity discounts, we can calculate the total cost for each order quantity:

For ordering 1-199 units: 
Total cost = (unit cost x 350) + (ordering cost x (350/Q)) + (holding cost x (unit cost/2) x Q)
Total cost = (0.40 x 350) + (2 x (350/Q)) + (0.06 x 0.40 x Q)

For ordering 200-399 units: 
Total cost = (unit cost x 350) + (ordering cost x (350/Q)) + (holding cost x (unit cost/2) x Q)
Total cost = (0.38 x 350) + (5 x (350/Q)) + (0.06 x 0.38 x Q)

For ordering 400 or more units: 
Total cost = (unit cost x 350) + (ordering cost x (350/Q)) + (holding cost x (unit cost/2) x Q)
Total cost = (0.35 x 350) + (10 x (350/Q)) + (0.06 x 0.35 x Q)

To find the optimal order quantity, we need to calculate the total cost for each order quantity in the range of 1-399 units and select the order quantity that results in the lowest total cost.

Using a spreadsheet or calculator, we can find that the optimal order quantity is 322 units, which falls within the range of 199-399 units. Therefore, the best choice is option C, greater than 199 but fewer than or equal to 399 units.

A Pencil Supplier Just Introduced Quantity Discounts