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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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Provides proofs for inventory costs.

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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 ...

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