Question

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?

a. 300
b. 306
c. 500
d. 200
e. None of the above

Answer 1

Answer:

a. 300

d. 200

Explanation:

EOQ = $\sqrt{(2 * Annual demand * ordering cost) / holding cost }$

2 * 7500 * 30 / 0.5

EOQ = 948 units

When price is $48 per unit

EOQ = 968 units

Total cost  = Holding cost + ordering cost + purchase cost

When the order is for 500 price is $48

Total cost = $2,400 + $30 + $24,000 = $26,430

When the order is for 300 price is $50

Total cost = $1,500 + $30 + $15,000 = $16,530

When the order is for 306 price is $50

Total cost = $1,530 + $30 + $15,300 = $16,860

When the order is for 200 price is $50

Total cost = $1,000 + $30 + $10,000 = $11,030

The best two possible order quantities are 200 and 300 which results in minimum total cost.