A beauty supply store expects to sell 120 flat irons during the next year. It costs $\$ 1.60$ to store one flat iron for one year. There is a fixed cost of $\$ 6$ for each order. Find the lot size and the number of orders per year that will minimize inventory costs.

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flat irons per order
orders per year

Step 1 ：This is a classic inventory management problem that can be solved using the Economic Order Quantity (EOQ) model. The EOQ model aims to determine the optimal order quantity that will minimize total inventory costs.

Step 2 ：The formula for EOQ is: \(EOQ = \sqrt{(2DS)/H}\) where: D = Demand rate per year, S = Ordering cost per order, H = Holding cost per unit per year.

Step 3 ：In this case, D = 120 flat irons, S = $6, and H = $1.60. We can plug these values into the EOQ formula to find the optimal order quantity.

Step 4 ：The number of orders per year can then be found by dividing the annual demand by the EOQ.

Step 5 ：Let's calculate this: D = 120, S = 6, H = 1.6, EOQ = 30.0, orders_per_year = 4.0

Step 6 ：Final Answer: The optimal lot size is \(\boxed{30}\) flat irons per order and the number of orders per year that will minimize inventory costs is \(\boxed{4}\).