The campus bookstore sells 4,000 sets of graduation regalia each year. Placing an order from their supplier costs $25 regardless of order quantity, so they usually place a large order (a half year's supply)at a time. It costs $5 per year to hold a cap and gown in inventory, primarily insurance costs for the highly flammable material. What is the difference in the total cost if they order at their optimal order quantity compared to their current policy?
A)$4,550
B)$5,050
C)$3,550
D)$4,050

Question

Quizplus · Accepted Answer

The optimal order quantity can be found using the Economic Order Quantity (EOQ) formula: $EOQ = \sqrt{\frac{2DS}{H}}$, where $D$ is the demand (4,000 sets/year), $S$ is the ordering cost ($25/order), and $H$ is the holding cost ($5/unit/year). Plugging in the values: $EOQ = \sqrt{\frac{2*4000*25}{5}} = \sqrt{40000} = 200$ sets. The total cost at EOQ includes ordering cost and holding cost. Ordering cost at EOQ is $D/Q*S = 4000/200*25 = $500$, and holding cost at EOQ is $Q/2*H = 200/2*5 = $500$. So, total cost at EOQ is $500 (ordering) + $500 (holding) = $1,000. Under their current policy (ordering twice a year, 2000 sets each time), the ordering cost is $2*25 = $50$, and the holding cost is $2000/2*5 = $5,000$. So, total cost under current policy is $50 (ordering) + $5,000 (holding) = $5,050. The difference in total cost is $5,050 (current policy) - $1,000 (EOQ) = $4,050.

The Campus Bookstore Sells 4,000 Sets of Graduation Regalia Each