A computer company sells motherboards for personal computers V For quantities up

ID: 349260 • Letter: A

Question

A computer company sells motherboards for personal computers V For quantities up through 25, the firm charges 350.00S per board; For quantities between 26 and 50, it charges 315S for each board purchased beyond 25; and, For quantities over 50. It charges 285S each large communications firm expects to require these motherboards at a rate of at least 140 per year. Order setup costs are 30.00S and Inventory holding costs are based on an 18 % annual interest rate. -/ What shonld be the size of the order?

Explanation / Answer

Given are following data :

Annual demand of motherboard = D = 140

Ordering cost = Co = $30

Annual unit holding cost = Ch = 18% of Price / unit

Therefore , Economic order quantity = Square root ( 2 x Co X D / Ch )

Since value of Ch changes with price and therefore every quantity range , there will a corresponding value of EOQ as per above formula for each of the quantity range. We need to check whether the calculated value of the EOQ falls within the Quantity Range t belongs to

Following table presents values of EOQs for various quantity levels :

Quantity range

Price / unit $)

Ch ( 18% of price/unit)

EOQ ( rounded to nearest whole number )

1 – 25

350

26 – 50

315

56.7

51 and above

285

51.30

Since calculated values of EOQ do not correspond to their respective Quantity Ranges as in 2nd and 3rd row, correct answer would be 12 as in first row,

Therefore , EOQ = 12 .

However EOQ = 12 as in 1st row is true only when we minimize total ordering cost and inventory holding cost

However we must take into account annual ordering cost also while calculating and comparing basis total cost

Following are the results :

For EOQ = 12 :

Annual ordering cost = Co x D/EOQ = $30 x 140/12 = $350

Annual inventory holding cost = Ch x EOQ/2 = $63 x 12/2 = $ 378

Annual purchase cost = Purchase price/ unit x Annual demand = $350 x 140 = $49,000

Therefore , Total cost = Annual ordering cost + Annual inventory holding cost + Annual purchase cost= $350 + $378 + $49,000 = $49728

For order quantity Q = 26 ( Beginning of second slab ) :

Annual ordering cost = Co x D/Q = $30 x 140/26 = $161.54

Annual inventory holding cost = Ch x Q/ 2 = $56.7 x 26 / 2 = $737.10

Annual purchase cost = Purchase price/ unit x Annual demand = $315 x 140 = $44100

Therefore , Total cost = Annual ordering cost + Annual inventory holding cost + Annual purchase cost

= $161.54+$737.10+$44100=$44998.64

For order quantity Q = 51 ( Beginning of third slab ) :

Annual ordering cost = Co x D/Q = $30 x 140/51 = $ 82.35

Annual inventory holding cost = Ch x Q/ 2 = $51.30 x 51/2 = $1308.51

Annual purchase cost = Purchase price/ unit x Annual demand = $285 x 140 = $39900

Therefore , Total cost = Annual ordering cost + Annual inventory holding cost + Annual purchase cost

= $82.35 + $1308.51 + $39900

= $41290.50

Out of above three options, the least cost option based on Total cost calculated as per above formula is for order quantity = 51. Therefore , size of the order should be 51

SIZE OF THE ORDER = 51