Final answer:
The economic order quantity is 66 units per order. There will be 33 orders placed per year. The total annual cost of managing the inventory is $313.00.
Step-by-step explanation:
The economic order quantity (EOQ) can be calculated using the following formula:
EOQ = √((2 * Annual Demand * Ordering Cost per Order) / Carrying Cost per Lamp)
Substituting the given values, we have:
EOQ = √((2 * 2200 * 0.50) / 20) = 66 units per order (rounded to the nearest whole number).
To determine the number of orders placed per year, we divide the annual demand by the economic order quantity:
Number of Orders = Annual Demand / EOQ = 2200 / 66 = 33.33. Therefore, Discount-Mart will place 33 orders per year (rounded to the nearest whole number).
The total annual cost of managing the inventory can be calculated by multiplying the number of orders by the ordering cost per order and adding it to the carrying cost per lamp multiplied by the economic order quantity:
Total Annual Cost = (Number of Orders * Ordering Cost per Order) + (EOQ * Carrying Cost per Lamp)
Substituting the given values, we have:
Total Annual Cost = (33 * 0.50) + (66 * 20) = $313.00 (rounded to the nearest whole number).