Final answer:
To minimize inventory costs, the retailer should use the Economic Order Quantity (EOQ) model. They should reorder approximately 496 units each time and reorder 8 times per year. The minimum inventory cost would be $7,048.
Step-by-step explanation:
To minimize inventory costs, the retailer should consider the Economic Order Quantity (EOQ) model. In the EOQ model, the reorder point is calculated using the formula:
Reorder point = Demand per period * Lead time
The retailer anticipates selling 3,900 units over the next year, which means the demand per period is 3,900 units / 1 year = 3,900 units/year. Since the retailer is charged a flat fee of $75 per order, the ordering cost is $75/order. The carrying cost per unit per year is $26. The EOQ formula is:
EOQ = sqrt((2 * demand * ordering cost) / carrying cost) = sqrt((2 * 3,900 * 75) / 26) ≈ 495.48
This means the retailer should reorder approximately 496 units each time. To find the number of times the retailer should reorder each year, we divide the total demand by the EOQ: 3,900 units / 496 units ≈ 7.86.
Since the retailer cannot reorder a fraction of a time, they should reorder 8 times per year with a lot size of 496 units. The minimum inventory cost can be calculated by multiplying the ordering cost per order by the number of orders per year and adding the carrying cost per unit per year multiplied by the average inventory level:
Minimum inventory cost = (ordering cost per order * number of orders) + (carrying cost per unit per year * average inventory)
For this retailer, the minimum inventory cost would be ($75 * 8) + ($26 * 496 / 2) = $600 + $6,448 = $7,048.