Question

16.8 Discount-Mart, a major East Coast retailer, wants to determine the economic order quantity (see Chapter 1210 for EOQ formulas) for its halogen lamps. It currently buys all halogen lamps from Specialty Lighting Manufacturers in Atlanta. Annual demand is 2,000 lamps, ordering cost per order is $30, and annual carrying cost per lamp is $12. a. What is the EOQ ? b. What are the total annual costs of holding and ordering (managing) this inventory? c. How many orders should Discount-Mart place with Specialty Lighting per year?

Answer 1

The economic order quantity (EOQ) for halogen lamps is approximately 110 lamps. The total annual costs of holding and ordering the inventory is $545.45. Discount-Mart should place 18 orders per year with Specialty Lighting.

Step-by-step explanation:

The formula to calculate the economic order quantity (EOQ) is given by:

EOQ = √((2 × Annual demand × Ordering cost per order) / Annual carrying cost per lamp)

Using the given information, we can calculate the EOQ as follows:

EOQ = √((2 × 2000 × 30) / 12) = √12000 = 109.54

Therefore, the EOQ for halogen lamps is approximately 110 lamps.

To calculate the total annual costs of holding and ordering the inventory, we can use the EOQ formula:

Total annual cost = (Ordering cost per order × Number of orders) + (EOQ × Annual carrying cost per lamp)

Using the given information and the EOQ we calculated earlier:

Total annual cost = (30 × (2000 / 110)) + (110 × 12) = $545.45

Therefore, the total annual costs of holding and ordering the inventory is $545.45.

Finally, to determine the number of orders Discount-Mart should place with Specialty Lighting per year, we can divide the annual demand by the EOQ:

Number of orders = Annual demand / EOQ = 2000 / 110 = 18.18

Since we cannot have fractional orders, Discount-Mart should place 18 orders per year with Specialty Lighting.

Answer 2

The EOQ for the halogen lamps is 100 lamps. The total annual costs of managing the inventory are $1,200. Discount-Mart should place 20 orders with Specialty Lighting per year.

Calculating the Economic Order Quantity (EOQ)

To calculate the EOQ for Discount-Mart, we will be using the EOQ formula given as EOQ = √((2DS)/H), where D is the annual demand, S is the ordering cost per order, and H is the annual carrying cost per unit.

Given the following:

• Annual demand (D) = 2,000 lamps
• Ordering cost per order (S) = $30
• Annual carrying cost per lamp (H) = $12

Plugging these values into the EOQ formula gives us:

EOQ = √((2 * 2000 * 30) / 12) = √(120,000 / 12) = √(10,000) = 100 lamps

b) The total annual costs of holding and ordering the inventory includes the carrying cost and ordering cost. The total annual carrying cost is the EOQ divided by 2, multiplied by the annual carrying cost per lamp. The total annual ordering cost is the annual demand divided by the EOQ, multiplied by the ordering cost per order. Total Annual Costs = (EOQ/2) * H + (D/EOQ) * S

Total Annual Costs = (100/2) * 12 + (2000/100) * 30 = 600 + 600 = $1,200

c) Discount-Mart should place the number of orders per year that results from dividing the annual demand by the EOQ.

Number of Orders = D / EOQ = 2000 / 100 = 20 orders per year

The complete question is here:

16.5Discount-Mart, a major East Coast retailer, wants to determine the economic order quantity (see Chapter 12 for EOQ formulas) for its halogen lamps. It currently buys all halogen lamps from Specialty Lighting Manufacturers, in Atlanta. Annual demand is 2,000 lamps, ordering cost per order is $30, annual carrying cost per lamp is $12.

a)What is the EOQ?

b)What are the total annual costs of holding and ordering (managing) this inventory?

c)How many orders should Discount-Mart place with Specialty Lighting per year?