Question

A repair shop orders gears from a supplier. The demand is 100,000 gears per year. There is a $1,000 charge for placing an order. The company has an inventory carrying cost equal to 20% of the cost of the inventory. The supplier has offered the following price discounts based on the quantity placed for each order. What order quantity will minimize the repair shop's total cost

Answer 1

7,071 gears

Step-by-step explanation:

As the cost of inventory has not been provided, hence I assumed the cost of one unit of Inventory is $20

The Economic order quantity will minimize the total costs

Use the following formula to calculate the Economic Order Quantity

Economic Order Quantity =
`\sqrt{(2DS)/(H) }`

Where

D = Demand = 100,000 gears

S = Cost per order = $1,000

H = Carrying cost per gear = $20 x 20% = $4

Placing values in the formula

Economic Order Quantity =
`\sqrt{(2 X 100,000 X 1,000)/(4) }`

Economic Order Quantity = 7,071 gears