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 optimal number of cases of beer that should be in each shipment, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula is derived from the trade-off between ordering costs and holding (or storage) costs.

The EOQ formula is given by:

EOQ = √((2 * D * S) / H)

Where:
D = Annual demand (450,000 cases/year)
S = Cost per order ($500)
H = Cost of holding or storing each case per year ($2)

We can now substitute the given values into the formula:

EOQ = √((2 * 450,000 * 500) / 2)

Simplifying the equation:

EOQ = √450,000 * 500
EOQ = √225,000,000
EOQ ≈ 15,000

Therefore, the optimal number of cases of beer that should be in each shipment to minimize ordering and storage costs is approximately 15,000 cases of beer per order.