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    EOQ- Proofs for total cost

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    3. Consider a DAG supermarket selling chicken noodle soup manufactured by the Campbell Soup Company. Customer demand for chicken noodle soup is R cans per year. The price Campbell charges is $C per can. DAG incurs a holding cost rate of {see attachment}. The ordering cost is $K per order. Using the EOQ formula, DAG normally orders in the following lot sizes: {see attachment}
    Campbell announces that it is offering a one-time-only discount of $d per can. Let Qd be the lot size ordered at the discounted price. Let t := Qd=Q¤.

    (See attached file for complete details)

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    https://brainmass.com/business/inventory/eoq-proofs-total-cost-13841

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    See attached file

    R= no of cans per year
    c= cost per can
    d= discount per can
    K= ordering cost
    Q*= economic order quantity
    alpha = holding cost

    a) Without discount

    Cost per year= Material Cost + Ordering Cost + Holding Cost
    Material Cost= cR
    Ordering Cost= (R/Q*) K
    Holding Cost= (Q*/2) c alpha

    Total cost per year= Material Cost + Ordering Cost + Holding Cost
    = cR + (R/Q*) K + (Q*/2) c alpha

    At the economic order quantity Ordering cost= Holding cost
    Thus

    (R/Q*) K = (Q*/2) c alpha

    So we can write total cost per year
    =cR + (R/Q*) K + (Q*/2) c alpha = cR + (Q*/2) c alpha + (Q*/2) c alpha = cR + Q* c alpha

    Total cost per year= cR + Q* c alpha

    Total cost in next t (Q */R) time units= (cR + Q* c alpha ) x t ...

    Solution Summary

    Provides proofs for inventory costs.

    $2.19

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