A product has a demand of 4000 units per year. Ordering cost is $20, and holding cost is $4 per unit per year. The EOQ model is appropriate. The cost-minimizing solution for this product will cost ________ per year in total annual inventory (holding and setup) costs.
A) $400
B) $800
C) $1200
D) Zero; this is a class C item.
E) Cannot be determined because the unit price is not known.

Question

Quizplus · Accepted Answer

The Economic Order Quantity (EOQ) model is used to find the optimal order quantity that minimizes total inventory costs, which include holding costs and ordering costs. The total cost is calculated using the formula: Total Cost = sqrt((2DS)/H), where D is the demand, S is the ordering cost, and H is the holding cost per unit. Plugging in the values given: Total Cost = sqrt((2*4000*20)/4) = sqrt(160000) = $400. However, this calculation gives us the optimal order quantity, not the total annual cost. The total annual cost involves both holding and ordering costs, which can be calculated using the formula: Total Annual Cost = sqrt(2DSH). So, Total Annual Cost = sqrt(2*4000*20*4) = sqrt(640000) = $800. This means the cost-minimizing solution for this product will cost $800 per year in total annual inventory costs.

A Product Has a Demand of 4000 Units Per Year