3. Sam's Watch Shop sells 2,500 watches a year. The store estimates that it costs $4 per year to carry a watch in inventory and $100 to place an order for watches. (a) Determine the total inventory costs associated with an order size of 500 and (b) compute the economic order quantity.
To determine the total inventory costs associated with an order size of 500, we need to calculate the carrying cost and the ordering cost.
(a) Carrying Cost:
The carrying cost is the cost of holding one unit of inventory for a year. In this case, the carrying cost is $4 per watch per year. Since the order size is 500, the total carrying cost would be:
Total carrying cost = Carrying cost per watch * Order size
= $4/watch * 500 watches
= $2000
(b) Ordering Cost:
The ordering cost is the cost of placing an order, which is given as $100 per order.
To compute the economic order quantity (EOQ), we can use the EOQ formula:
EOQ = sqrt[(2 * annual demand * ordering cost) / carrying cost]
Where:
- Annual demand is the number of watches sold in a year, which is given as 2,500.
- Ordering cost is the cost of placing an order, which is $100.
- Carrying cost is the cost of holding one unit of inventory for a year, which is $4 per watch.
Plugging in these values:
EOQ = sqrt[(2 * 2500 * 100) / 4]
= sqrt[(500,000) / 4]
= sqrt[125,000]
≈ 353.55
Therefore, the economic order quantity is approximately 353.55 watches.