A retail outlet for calculators sells 900 calculators per year. It costs $\$ 2$ to store one calculator for a year. To reorder, there is a fixed cost of $\$ 4$, plus $\$ 2.25$ for each calculator. How many times per year should the store order calculators, and in what lot size, in order to minimize inventory costs?
The store should order calculators times per year to minimize inventory costs. (Simplify your answers.)
Answer
Final Answer: The store should order calculators 15 times per year with a lot size of 60 calculators each time to minimize inventory costs. So, the answers are \(\boxed{15}\) and \(\boxed{60}\).
Step 1 ：This problem is about inventory management, specifically an Economic Order Quantity (EOQ) problem. The EOQ model aims to determine the optimal order quantity that will minimize total inventory costs. The total cost is the sum of the ordering cost and the holding cost. The ordering cost is the cost of placing an order and is assumed to be fixed. The holding cost is the cost to hold an item in inventory for a given period of time.
Step 2 ：The formula for EOQ is given by: \[EOQ = \sqrt{\frac{2DS}{H}}\] where: D = Demand rate per period, S = Setup or order cost per order, H = Holding or carrying cost per unit per period.
Step 3 ：In this case, D = 900 calculators per year, S = $4 per order, and H = $2 per calculator per year.
Step 4 ：Substituting these values into the EOQ formula, we get: \[EOQ = \sqrt{\frac{2*900*4}{2}} = 60.0\]
Step 5 ：The number of orders per year is given by D/EOQ. Substituting the values, we get: \[orders\_per\_year = \frac{900}{60} = 15.0\]
Step 6 ：Final Answer: The store should order calculators 15 times per year with a lot size of 60 calculators each time to minimize inventory costs. So, the answers are \(\boxed{15}\) and \(\boxed{60}\).
