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
To determine the number of cases of beer per order, we need to calculate the Economic Order Quantity (EOQ). The EOQ formula is as follows:
EOQ = √(2DS/H)
Where:
D = Annual demand (in units)
S = Ordering cost per order
H = Holding cost per unit per year
Given the information:
Annual demand (D) = 450,000 cases
Ordering cost per order (S) = $500
Holding cost per unit per year (H) = $2
Let's calculate the EOQ:
EOQ = √(2 * 450,000 * 500 / 2)
EOQ = √(450,000 * 500)
EOQ ≈ √225,000,000
EOQ ≈ 15,000
Therefore, Lehen Vinters should order approximately 15,000 cases of beer per shipment to minimize ordering and storage costs.