Question

Item X is a standard item stocked in a company's inventory component parts. each year the firm, on a random basis, uses about 1600 of item x, which costs $25 each. Storage cost, which include insurance and cost of capital amount to $6 per unit of average inventory. Every time an order is placed for more of item X it cost $12.

When item x is ordered, what should the order size be?

What is the annual cost for ordering item X

Answer 1

The optimal order size for item X is 80 units using the Economic Order Quantity (EOQ) formula. The annual cost for ordering item X is $240, calculated by dividing the total annual demand by the EOQ and multiplying by the cost per order.

Step-by-step explanation:

To determine the optimal order size for item X, we can use the Economic Order Quantity (EOQ) model. The EOQ model is a formula used to calculate the most cost-effective quantity to order.

In this case, we have an annual demand (D) of 1600 units, a cost per order (S) of $12, and a holding cost per unit per year (H) of $6.

The EOQ formula is given by:

EOQ = sqrt((2DS)/H)

Plugging in the values, we have:

EOQ = sqrt((2*1600*12)/6) = sqrt(6400) = 80 units.

The optimal order size is therefore 80 units of item X.

Next, to calculate the annual cost of ordering item X, we take the total annual demand and divide it by the EOQ to determine how many times we'll order per year. Then we multiply by the cost per order:

Annual Ordering Cost = (D/EOQ) * S

= (1600/80) * 12

= 20 * 12

= $240.

Thus, the annual cost for ordering item X is $240.