6-20 Lila Battle has determined that the annual demand for number 6 screws is 10

Question

6-20 Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $10 ev- ery time an order is placed. This cost includes her wages, the cost of the forms used in placing the or- der, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is con- stant throughout the year (a) How many number 6 screws should Lila order at a time if she wishes to minimize total inventory cost? (b) How many orders per year would be placed? What would the annual ordering cost be? (c) What would the average inventory be? What would the annual holding cost be

Explanation / Answer

Ans a – Economic order quantity = SQRT (2 x demand x Oder cost / Carrying cost) = SQRT (2 x 100000 x 10 / 0.005) = 20000 units.

Ans b – Orders = Annual demand / EOQ = 100000 / 20000 = 5 orders

Ans c – Annual Ordering cost = 5 x 10 = $50

Ans d – Average inventory = EOQ / 2 = 20000 / 2 = 10000 units

Ans e – Annual holding cost = average inventory x holding cost per unit per year = 10000 x 0.005 = $50.

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