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
E)None of the above

Question

Quizplus · Accepted Answer

To find the two possible order quantities, we need to use the Economic Order Quantity (EOQ) formula:

EOQ = sqrt(2DS/H)

Where:
D = annual demand = 7,500 units
S = ordering cost = $30 per order
H = holding cost as a percentage of purchase cost = 10% of $50 = $5

Plugging in the values, we get:

EOQ = sqrt(2*7,500*30/5) = sqrt(90,000) = 300

This gives us one possible order quantity. However, we also need to check if it's cheaper to order 500 units instead, since the price per unit drops to $48 at that quantity.

Total Cost for ordering 300 units = TC1
Total Cost for ordering 500 units = TC2

TC1 = Total annual ordering cost + Total annual holding cost
TC1 = [(7500/300)*30] + [(300/2)*50*0.1]
TC1 = 750 + 750
TC1 = $1500

TC2 = Total annual ordering cost + Total annual holding cost
TC2 = [(7500/500)*30] + [(500/2)*48*0.1]
TC2 = 450 + 1200
TC2 = $1650

As we can see, ordering 300 units is cheaper than ordering 500 units. Therefore, the two possible order quantities are 300 and 500, and the best choice is to order 300 units.

RCBarker Makes Purchasing Decisions for His Company