Question

Rico needs 597 lbs of roast beef per week on average to make sandwiches for his cafe. The supplier charges a $24 delivery fee per order (which is independent of the order size) and $5.78 per lb. Rico’s annual holding cost is 27%. Assume 52 weeks per year. If Rico wants to minimize inventory holding and ordering costs, how much roast beef should he purchase with each order (in lbs)? (report your answer as an integer)

Answer 1

Rico should order approximately 979 lbs of roast beef with each order to minimize inventory holding and ordering costs, using the Economic Order Quantity model.

Step-by-step explanation:

To determine how much roast beef Rico should purchase with each order to minimize inventory holding and ordering costs, we apply the Economic Order Quantity (EOQ) model. The EOQ model helps businesses minimize the total cost of inventory management, which includes ordering costs (such as delivery fees) and holding costs (such as storage and insurance).

The formula for EOQ is:
EOQ = √((2DS)/H),
where:
D = Demand (how much stock is needed over a certain period),
S = Ordering cost per order,
H = Holding cost per unit per period.

In Rico's case:
D = 597 lbs per week * 52 weeks per year = 31,044 lbs per year,
S = $24 per order,
H = 27% of cost per lb per year = 0.27 * $5.78 = $1.5606 per lb per year.

Plugging in the values:
EOQ = √((2 * 31,044 * 24) / 1.5606) ≈ √(1,497,904 / 1.5606) ≈ √957,665.991 ≈ 978.60 lbs.

Rico should therefore order approximately 979 lbs (rounded to the nearest integer) of roast beef with each order.