A service garage uses 120 boxes of cleaning cloths a year. The boxes cost $6 each. Ordering cost is $3 and holding cost is 10 percent of purchase cost per unit on an annual basis. Determine:(A) the economic order quantity (B) the total cost of carrying the cloths (excluding purchase price)

(A) The economic order quantity is 35 units

(B) The total cost of carrying the cloths (excluding purchase price) is $20.78

Explanation:

According to the given data we have the following:

D = Demand rate, units per year = 120

S = Cost per order placed, or setup cost = $3

C = Unit cost, dollars per unit = $6

i = Carrying rate, percent of value per year = 10%

A)Therefore in order to calculate the economic order quantity we have to use the following formula:

economic order quantity is Q = Sqrt [(2*S*D)/(i*C)]

Q = Sqrt {(2*3*120)/(10%*6)} = 35 units

B) The total cost of carrying the cloths (excluding purchase price) =Ordering cost+Carrying cost per year

Ordering cost = (cost per order) x orders per year) = SD/Q = 3*120/35 = $10.28

Carrying cost per year = (annual carrying rate) x (unit cost) x average inventory = iCQ/2 = 10%*6*35/2 = $10.5

Therefore, The total cost of carrying the cloths  = 10.28+10.50 = $20.78

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