Table 1
Peterson Enterprises uses a fixed order quantity inventory control system. The firm operates 50 weeks per year and has the following characteristics for an item:
Demand $= 50,000$ units/year
Ordering cost $= \$ 35 /$ order
Inventory-carrying cost as a percent of item value $= 25 \%$
Item (Unit) value $= \$ 8$
Lead time $= 3$ weeks
Standard deviation in weekly demand $= 125$ units
-The total order and inventory-holding cost is:
A) less than $1,000.
B) more than or equal to $1,000 but less than $1,500.
C) more than or equal to $1,500 but less than $2,000.
D) more than or equal to $2,000.

Question

Quizplus · Accepted Answer

First, calculate the Economic Order Quantity (EOQ) to find the optimal order size, then use it to calculate the total order and inventory-holding costs. EOQ = $\sqrt{(2DS)/H}$, where D is demand, S is the ordering cost, and H is the holding cost per unit per year. Here, D = 50,000 units/year, S = $35/order, and H = 25% of item value = 25% of $8 = $2. The EOQ = $\sqrt{(2*50000*35)/2} = \sqrt{3500000} \approx 1870$ units/order. Total order cost = $D/EOQ * S = 50000/1870 * 35$, and total holding cost = $EOQ/2 * H$. Both calculations show that the costs are significantly above $1,000, leading to the conclusion that the total cost is more than $2,000.

Table 1 Peterson Enterprises Uses a Fixed Order Quantity Inventory =50,000= 50,000=50,000

Table 1
Peterson Enterprises Uses a Fixed Order Quantity Inventory $= 50,000$