The annual demand for a product has been projected at 2,000 units.This demand is assumed to be constant throughout the year.The ordering cost is $20 per order,and the holding cost is 20 percent of the purchase cost.Currently,the purchase cost is $40 per unit.There are 250 working days per year.Whenever an order is placed,it is known that the entire order will arrive on a truck in 6 days.Currently,the company is ordering 500 units each time an order is placed.What is the total holding cost for the year using this policy?
A)$400
B)$2,000
C)$4,000
D)$8,000
E)None of the above

Question

Quizplus · Accepted Answer

First, we need to calculate the optimal order quantity. We can use the Economic Order Quantity (EOQ) formula:

EOQ = √((2DS)/(H))

where:
D = annual demand = 2,000
S = ordering cost = $20
H = holding cost as a percentage of purchase cost = 20% of $40 = $8

Plugging in the values, we get:

EOQ = √((2*2,000*20)/8) = 100 units

Next, we need to calculate the number of orders per year:

Number of orders = D/EOQ = 2,000/100 = 20 orders

The time between orders (i.e., the order cycle) is:

Order cycle = number of working days per year / number of orders = 250/20 = 12.5 days

This means that we should order 100 units every 12.5 days, which is equivalent to 20 orders per year.

The total holding cost for the year can be calculated as:

Total holding cost = average inventory level * holding cost per unit

To find the average inventory level, we can use the EOQ formula:

EOQ/2 = 50 units

Since we're ordering 100 units per order, this means that we'll have 50 units in inventory at any given time. Therefore, the average inventory level is:

Average inventory level = 50 units

The holding cost per unit is 20% of $40, or $8.

Total holding cost = 50 * $8 * 20 = $8,000

Therefore, the total holding cost for the year using this policy is $8,000. However, this is much higher than the holding cost for other policies, which suggests that there may be a better choice.

The Annual Demand for a Product Has Been Projected at 2,000