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 hold 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 (4)days. If the order size was 1,000 kilograms of resin,what would be the average inventory level?
A)50 kilograms
B)200 kilograms
C)500 kilograms
D)800 kilograms
E)1,000 kilograms

Question

Quizplus · Accepted Answer

The usage rate is given as 50 kilograms per day. Therefore, the weekly usage is (50 kg/day X 7 days =) 350 kilograms per week. The order lead time is also given as 4 days. This means that the materials manager must place an order every (4 days + 7 days =) 11 days.

To calculate the optimal order quantity using the Economic Order Quantity (EOQ) model, we can use the following formula:

EOQ = sqrt((2 x demand x order cost) / holding cost per unit)

where demand = the annual demand for the item, order cost = the cost of placing an order, and holding cost per unit = the cost of holding one unit of inventory for a year.

Using the given information, we can calculate the EOQ as follows:

Annual demand = 350 kg/week x 52 weeks/year = 18,200 kg/year
Order cost = $100/order
Holding cost per unit = $0.04/kg/day x 365 days/year = $14.60/kg/year

EOQ = sqrt((2 x 18,200 kg/year x $100/order) / $14.60/kg/year) = 983 kg

Since the order size is 1,000 kg, this is close to the optimal EOQ. Therefore, the average inventory level can be estimated as half of the order quantity, i.e., (1,000 kg / 2 =) 500 kg. Therefore, the correct answer is (C) 500 kilograms.

The Materials Manager for a Billiard Ball Maker Must Periodically