Part of your business is selling modems for network connection. Demand for modems in your store is about 8,000 units per year. Ordering a shipment of modems costs about $500 in processing. A modem costs you $150 and holding a modem in inventory costs you 12% of its cost per year. Now assume that the supplier gives you the following discount schedule:0-499 $150500-999 $1491000-1999 $1482000-4999 $1475000 - $146What is the total annual inventory/ordering cost for this quantity?

If the firm buys at the least price $146

Annual demand (D) = 8,000 units

Ordering cost per order (Co) = $500

Holding cost per item per annum (H) = 12% x $146 = $17.52

EOQ = √ 2DCo

H

EOQ = √ 2 x 8,000 x $500

$17.52

EOQ = 676 units

The solution is not feasible since 676 units cannot be bought at $146. Thus, EOQ is 5,000 units.

Total cost of 5,000 units

= Total ordering cost + Total holding cost + Total purchase cost

= DCo + QxH + Price x Annual demand

Q 2

= 8,000 x $500 + 5,000 x $17.52 + $146 x 8,000

5,000 2

= $800 + $43,800 + $1,168,000

= $1,212,600

Explanation:

In this case, we need to calculate the EOQ at the lowest price offered by the supplier. The lowest price gives the minimum total cost. EOQ equals square root of 2 multiplied by annual demand and ordering cost per order divided by holding cost per item per annum. The holding cost per item per annum is calculated as 12% of the price of $146.

The calculated EOQ of 676 units is not feasible because the quantity does not qualify for the price of $146. The minimum price that could be bought at $146 is 5,000 units. Thus, it becomes the EOQ.

Total cost is calculated as total ordering cost plus total holding cost plus total purchase cost. The company should buy 5,000 units at $146 in order to minimize the total cost.

Total inventory procuring cost $ 12.000

Explanation:

Step 1. Given information. and Step 2. Formulas needed to solve the exercise.

To find out invencoty cost, we need to calculate EQO

EOQ = sqrt of (2 * ordering cost per order * total quantity required / carrying cost per order)

Total inventory procuring cost = Carrying cost per unit per year (EOQ/2) + Fixed order cost * no of times ordered

Step 3. Calculation. and Step 4. Solution.

EOQ = sqrt of (2 * 500 * 8.000 / 18) = 667 units.

Therefore no of times to be ordered = 8.000/667 = 11.99 = 12 times

Total inventory procuring cost = 18 (667/2) + 500 (8.000/667) = $ 12.000

Note

Total Inventory procuring Cost is the sum of the carrying cost and the ordering cost of inventory.