Question

Suppose that the demand rate is 500 units per week. The fixed ordering cost is $60 per order. The unit inventory cost is 20% of the product cost. The cost of the product depends on the quantity ordered. It is $0.05 when you order less than 2300 units, $0.048 when you order between 2301 and 5000 units and $0.045 when you order more than 3000 units. What is your optimal order quantity if you intend to limit the number of units to at or below 2300 units

Answer 1

Optimal order quantity is 17,664 units

Step-by-step explanation:

Optimal order quantity is the quantity at which business incur minimum cost. This is the level of order where the holding cost equals to the ordering cost of the business.

As per given Data

Demand = 500 units per week = 500 units x 52 weeks = 26,000 units

Ordering Cost = $60

As the limit of the is 2,300 or below the product cost is $0.05 and the inventory cost is 20% of the product cost.

Inventory cost = $0.05 x 20% = $0.01

Optimal order quantity =
`\sqrt{(2 X Ordering cost X Annual Demand)/(Inventory cost) }`

Optimal order quantity =
`\sqrt{(2 X 60 X 26000)/(0.01) }`

Optimal order quantity = 17,664 units