Question

Rico needs 882 lbs of roast beef per week on average to make sandwiches for his cafe. The supplier charges a $15 delivery fee per order (which is independent of the order size) and $12.81 per lb. Rico’s annual holding cost is 26%. 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 907 lbs of roast beef with each order to minimize inventory holding and ordering costs, according to the Economic Order Quantity model.

Step-by-step explanation:

To calculate the amount of roast beef Rico should purchase with each order to minimize inventory holding and ordering costs, we need to use the Economic Order Quantity (EOQ) model. The formula for EOQ is √((2DS)/H), where D is the annual demand, S is the ordering cost per order, and H is the annual holding cost per unit. Rico’s annual demand is 882 lbs per week multiplied by 52 weeks, which equals 45,864 lbs. The ordering cost S is $15 per order, and the annual holding cost H is 26% of the cost per pound of beef ($12.81), so H equals 0.26 * $12.81 or approximately $3.33 per lb per year.

Plugging these values into the EOQ formula gives us: √((2 * 45,864 lbs * $15 order) / $3.33 lb/year) ≈ √((2 * 45,864 * 15) / 3.33) ≈ √(2736470 / 3.33) ≈ √821991.59 ≈ 906.65. Since the ordering quantity must be an integer, Rico should order 907 lbs of roast beef with each order to minimize costs.