Lehen Vinters imports a certain brand of beer. The demand, which may be assumed to be uniform, is 450,000 cases/year. The cost of ordering a shipment of beer is $500, and the cost of storing each case of beer for a year is $2. Determine how many cases of beer should be in each shipment if the ordering and storage costs are to be kept at a minimum. (Assume that each shipment of beer arrives just as the previous one has been sold.)

Question

Lehen Vinters imports a certain brand of beer. The demand, which may be assumed to be uniform, is 450,000 cases/year. The cost of ordering a shipment of beer is $500, and the cost of storing each case of beer for a year is $2. Determine how many cases of beer should be in each shipment if the ordering and storage costs are to be kept at a minimum. (Assume that each shipment of beer arrives just as the previous one has been sold.)

? cases of beer per order

Answer 1

To determine the number of cases of beer per order that minimizes the ordering and storage costs, we need to find the Economic Order Quantity (EOQ). EOQ is the optimal order quantity that minimizes the total cost of ordering and holding inventory.

The formula to calculate EOQ is:

EOQ = √((2 * D * S) / H)

Where:
D = Annual demand (in cases)
S = Cost per order
H = Holding cost per case per year

Given values:
D = 450,000 cases/year
S = $500/order
H = $2/case/year

Plugging in the values into the formula, we can calculate the EOQ:

EOQ = √((2 * 450,000 * 500) / 2)
= √(450,000,000 / 2)
= √225,000,000
≈ 15,000 cases

Therefore, Lehen Vinters should order approximately 15,000 cases of beer per order to minimize the ordering and storage costs.