New England Charm,Inc.specializes in selling scented candles.The company has established a policy of reordering inventory every 30 days.A recently employed MBA has considered New England's inventory problem from the EOQ model viewpoint.If the following constitute the relevant data,how does the current policy compare with the optimal policy? $\begin{array}{ll}
\text { Ordering cost } & =\$ 10 \text { per order } \
\text { Carrying cost } & =20 \% \text { of purchase price } \
\text { Purchase price } & =\$ 10 \text { per unit } \
\text { Total sales for year } & =1,000 \text { units } \
\text { Safety stock } & =0
\end{array}$

Question

Quizplus · Accepted Answer

To find the Economic Order Quantity (EOQ), we use the formula: $$EOQ = \sqrt{\frac{2DS}{H}}$$ where $D$ is the demand (1,000 units), $S$ is the ordering cost (\$10 per order), and $H$ is the carrying cost per unit (\$2, calculated as 20% of the \$10 purchase price). Plugging in the values: $$EOQ = \sqrt{\frac{2 \times 1000 \times 10}{2}} = \sqrt{10000} = 100 \text{ units}$$ The company orders every 30 days, implying 12 orders per year (365/30 ≈ 12). With EOQ, the number of orders would be $D/EOQ = 1000/100 = 10$ orders per year. The total cost under EOQ includes ordering and carrying costs: $$Total \, EOQ \, Cost = \frac{D}{Q}S + \frac{Q}{2}H = \frac{1000}{100} \times 10 + \frac{100}{2} \times 2 = 100 + 100 = \$200$$ Under the current policy (ordering every 30 days, 12 times a year), the order quantity is $1000/12 ≈ 83.33$ units. The total cost is: $$Total \, Current \, Cost = \frac{D}{Q}S + \frac{Q}{2}H = \frac{1000}{83.33} \times 10 + \frac{83.33}{2} \times 2 ≈ 120 + 83.33 = \$203.33$$ The difference in total costs is $203.33 - 200 = \$3.33$, which rounds to \$3, indicating that total costs under the current policy exceed those under the EOQ by approximately $3.

New England Charm,Inc A)Total Costs Will Be the Same, Since the Current Policy