Question

Technology Corporation expects to order 126,000 memory chips for inventory during the coming year, and it will use this inventory at a constant rate. Fixed ordering costs are $200 per order; the purchase price per chip is $25; and the firm’s inventory carrying costs is equal to 20 percent of the purchase price. (Assume a 360-day year.) What is the economic ordering quantity for chips? Enter your answer rounded to two decimal places. For example, if your answer is 12.345 then enter as 12.35 in the answer box.

Answer 1

Solution:

Economic order quantity is calculated using the following formula:

= ( 2AO / C ) ^{( ½ )}

Where A = Annual usage units

O = Ordering cost per unit

C = Annual carrying cost of one unit i.e., (Carrying cost percentage * cost of one unit)

In the given question as per the data given:

Purchase price per unit = $ 25

A = Annual usage units = 126,000

O = Ordering cost per unit = $ 200

C = Annual Inventory carrying cost of one unit = $ 25 * 20 % = $ 5

Applying the above values in the formula we have :

Thus Economic order quantity = ( ( 2* 126,000 * $ 200 ) / 5 ) ^{( ½ )}  

= ( 50,400,000 / 5 ) ^{( ½ )}

= ( 10,080,000 ) ^{( ½ )}

= 3,174.9016 ( when rounded off to four decimal places )

= 3,174.90 ( when rounded off to two decimal places )

Thus the Economic Order Quantity of chips = 3174.90

Note : The square root of 10,080,000 is calculated using the following formula in excel

=SQRT(Number) = SQRT(10,080,000) = 3174.9016