# EOQ- Proofs for total cost

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=QÂ¤.

(See attached file for complete details)

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#### Solution Preview

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.