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27 January, 14:57

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)

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  1. 27 January, 16:06
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    (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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