Question

A warehouse sells 10,000 boxes of copy paper per year. It costs $150 to reorder from the factory. Each box costs $5, and the holding cost rate is 0.35 per year. Find the optimal order quantity, theaverage inventory cost, the number of orders placed per year, and the inventory cost per year. Assume a lead time of 2 weeks.

Answer 1

Calculating the optimal order quantity using the Economic Order Quantity formula results in approximately 245 boxes, with an average inventory cost of about $214.38, about 41 orders placed per year, and an inventory cost per year of approximately $7,562.50.

Step-by-step explanation:

The optimal order quantity for this warehouse scenario can be calculated using the Economic Order Quantity (EOQ) formula, which is √(2DS/H), where D is the annual demand, S is the ordering cost, and H is the holding cost per unit per year. In this case, the annual demand (D) is 10,000 boxes, the ordering cost (S) is $150, and the holding cost per unit per year (H) is 0.35 times the cost per unit, which is $5, so H equals $1.75. Plugging these values into the EOQ formula gives us √(2*10000*150/1.75), resulting in an optimal order quantity of approximately 245 boxes per order.

The average inventory cost is half of the EOQ multiplied by the holding cost per unit, which is (245/2)*1.75, equating to approximately $214.38. The number of orders placed per year is the annual demand divided by the EOQ, which gives us 10,000/245, resulting in about 41 orders per year. Lastly, the inventory cost per year can be calculated by summing up the ordering and holding costs, which is 41*$150 + 122.5*$1.75, totaling approximately $7,562.50.