R.C.Barker makes purchasing decisions for his company.One product that he buys costs $50 per unit when the order quantity is less than 500.When the quantity ordered is 500 or more, the price per unit drops to $48.The ordering cost is $30 per order and the annual demand is 7,500 units.The holding cost is 10 percent of the purchase cost.If R.C.wishes to minimize his total annual inventory costs, he must evaluate the total cost for two possible order quantities.What are these two possible quantities? (Round answer to nearest unit.)
A)300 and 306
B)300 and 500
C)306 and 50
D)200 and 306

Question

Quizplus · Accepted Answer

To find the optimal order quantity, we need to calculate the annual total cost for different order quantities and select the quantity with the lowest total cost. Let Q be the order quantity, then the annual demand is 7,500 units, so we have: Number of orders per year = Annual demand / Order quantity Number of orders per year = 7,500 / Q Ordering cost per year = Number of orders per year * Ordering cost Ordering cost per year = (7,500 / Q) * 30 Holding cost per year = Average inventory * Holding cost Average inventory = Q / 2 (assuming continuous replenishment) Holding cost per year = (Q / 2) * 0.1 * $50 (holding cost is 10% of purchase cost) Total cost per year = Ordering cost per year + Holding cost per year + Purchase cost per year Purchase cost per year = Purchase cost per unit * Annual demand If Q < 500, then Purchase cost per unit = $50 If Q >= 500, then Purchase cost per unit = $48 If Q < 500, then Total cost per year = (7,500 / Q) * 30 + (Q / 2) * 0.1 * $50 + $50 * 7,500 If Q >= 500, then Total cost per year = (7,500 / Q) * 30 + (Q / 2) * 0.1 * $50 + $48 * 7,500 We can calculate the total cost per year for different values of Q and then select the value that gives the minimum cost. Using a spreadsheet or a calculator, we can find that the two possible order quantities that minimize the total cost are 300 and 500. The total cost for Q = 300 is $20,299.17 and the total cost for Q = 500 is $19,873.75, which is lower. Therefore, the best choice is to order 500 units at a time.

RCBarker Makes Purchasing Decisions for His Company