Question

A jeweler purchases silver for use in its products. The firm uses 200 grams of silver per week and purchases silver for $0.54 per gram from a supplier. Each time the firm orders silver from the supplier, the firm must pay an order processing charge of $10. The firm's annual holding cost percentage is 37%. If the jeweler orders 2,000 grams of silver with each order, what is the sum of the annual holding and ordering costs?

Answer 1

The sum of the annual holding and ordering costs for the jeweler can be calculated by adding the ordering cost and the holding cost. The ordering cost includes the order processing charge and the cost of each order, while the holding cost is determined by the average inventory level and the holding cost percentage. By calculating the number of orders per year and multiplying it by the ordering cost per order, then adding it to the holding cost, the sum of the annual holding and ordering costs can be determined.

Step-by-step explanation:

To determine the sum of the annual holding and ordering costs for the jeweler, we need to calculate the ordering cost and the holding cost separately.

The ordering cost is the sum of the order processing charge and the cost of each order. Since the jeweler orders 2,000 grams of silver with each order, the cost of each order is 2,000 grams multiplied by the cost per gram, which is $0.54. Therefore, the ordering cost per order is $0.54 * 2,000 = $1,080. Adding the order processing charge of $10, the total ordering cost per order is $1,090.

The holding cost is calculated by multiplying the average inventory level by the holding cost percentage. The average inventory level can be calculated by dividing the order quantity by 2, since the jeweler orders 2,000 grams and uses 200 grams per week. Therefore, the average inventory level is 2,000 / 2 = 1,000 grams. Multiplying the average inventory level by the holding cost percentage of 37% gives us the holding cost.

Finally, we can calculate the sum of the annual holding and ordering costs by multiplying the total ordering cost per order by the number of orders per year and adding it to the holding cost. The number of orders per year can be calculated by dividing the total demand per year by the order quantity. In this case, the total demand per year is 200 grams per week multiplied by 52 weeks = 10,400 grams. Dividing this by the order quantity of 2,000 grams gives us 10,400 / 2,000 = 5.2 orders per year.

Therefore, the sum of the annual holding and ordering costs is ($1,090 * 5.2) + (1,000 grams * 37% * $0.54).