Question

​Discount-Mart, a major East Coast​ retailer, wants to determine the economic order quantity for its halogen lamps. It currently buys all halogen lamps from Specialty Lighting​ Manufacturers, in Atlanta. Annual demand is 2200 lamps, ordering cost per order is $0.50​, carrying cost per lamp is $20.As part of its new JIT​ program, Discount-Mart has signed a​ long-term contract with Specialty Lighting and will place orders electronically for its halogen lamps.

a) What is the economic order​ quantity? ___ units per order​(round your response to the nearest whole​ number).
​b) How many orders will be​ placed? ___ per year ​(round your response to the nearest whole​ number).
​c) What is the total annual cost of managing the inventory with this​ policy?___ $ ​(round your response to the nearest whole​ number).

Answer 1

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).

Answer 2

The Economic Order Quantity for halogen lamps is 47 units per order. Discount-Mart will place approximately 47 orders per year. The total annual cost of managing the inventory with this policy is about $494.

Step-by-step explanation:

To solve for the Economic Order Quantity (EOQ), we use the EOQ formula:
EOQ = √((2DS)/H) where D is the annual demand, S is the ordering cost per order, and H is the carrying cost per unit.

1. Determine the EOQ: D = 2200 lamps, S = $0.50, H = $20 per lamp.
   EOQ = √((2 * 2200 * 0.50)/20) = √(2200) = 46.9 ≈ 47 units per order.
2. Calculate the number of orders per year: Number of Orders = D/EOQ = 2200/47 ≈ 46.81 ≈ 47 orders per year.
3. Compute the total annual cost: Total Annual Cost = (Order Cost * Number of Orders) + (Carrying Cost * Average Inventory Level) = (0.50 * 47) + (20 * (47/2)) = $23.5 + $470 = $493.5 ≈ $494.