The materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. She knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. She also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four days. What is the economic order quantity for resin?
A)50 kilograms
B)100 kilograms
C)250 kilograms
D)500 kilograms
E)1,000 kilograms

Question

Quizplus · Accepted Answer

The Economic Order Quantity (EOQ) formula is given by $\sqrt{\frac{2DS}{H}}$, where $D$ is the annual demand, $S$ is the ordering cost per order, and $H$ is the holding cost per unit per year. In this scenario, $D = 50 \text{ kg/day} \times 365 \text{ days/year} = 18,250 \text{ kg/year}$, $S = $100$, and $H = $0.04$. Plugging these values into the EOQ formula gives $\sqrt{\frac{2 \times 18,250 \times 100}{0.04}} = \sqrt{912,500,000} = 30,208.33$. This doesn't match any of the options provided, indicating a mistake in my calculation. Let's correct the calculation:Correct calculation: $D = 50 \text{ kg/day} \times 365 \text{ days/year} = 18,250 \text{ kg/year}$, $S = $100$, and $H = $0.04$. The correct EOQ calculation should be $\sqrt{\frac{2 \times 18,250 \times 100}{0.04}}$.However, the mistake was in the interpretation of the calculation result. The correct approach to find the EOQ involves using the given formula and correctly interpreting the given data:Given that the daily usage rate of resin is 50 kilograms, and assuming a 365-day year for simplicity, the annual demand $D$ is $50 \times 365 = 18,250$ kilograms. The order cost $S$ is $100 per order, and the holding cost $H$ is $0.04 per kilogram per day, which translates to $0.04 \times 365 = $14.60$ per kilogram per year.Plugging these values into the EOQ formula gives:$$EOQ = \sqrt{\frac{2 \times 18,250 \times 100}{14.60}} = \sqrt{\frac{3,650,000}{14.60}} \approx \sqrt{250,000} \approx 500 \text{ kilograms}.$$Therefore, the correct answer is 500 kilograms, which matches option D. My initial explanation contained a calculation error, and upon correction, the accurate EOQ calculation indeed points to option D as the correct answer.

The Materials Manager for a Billiard Ball Maker Must Periodically