HK3 Xiaoliang Liu - 1 a TC(2Q)=(R\/2Q)S(2Q\/2)hC=(R\/2Q)S(Q)hC TC(Q)=(R\/Q)S(Q\/2)hC Q = EOQ therefore(R\/Q)S=(Q\/2)hC TC(2Q\/TC(Q)=(R\/2Q)S(Q)hC(R\/Q)S(Q\/2

HK3 Xiaoliang Liu - 1 a...

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1. a. TC ( 2 Q ) = ( R /2 Q ) S + ( 2 Q /2 ) hC= ( R /2 Q ) S + ( Q ) hC TC ( Q )=( R / Q ) S + ( Q /2 ) hC Q = EOQ, therefore, ( R / Q ) S= ( Q /2 ) hC TC ( 2 Q ) / TC ( Q ) =( ( R /2 Q ) S + ( Q ) hC) /( ( R / Q ) S+ ( Q /2 ) hC)=5/4 b. TC ( Q /2 )= ( R / (Q /2) ) S + (( Q /2)/2 ) hC= (2 R / Q ) S + ( Q /4 ) hC TC ( Q /2 ) / TC ( Q ) =( (2 R / Q ) S + ( Q /4 ) hC) / ( ( R / Q ) S + ( Q /2 ) hC)=5/4 c. Whenever Q is increase or decrease, TC(Q) all increase. Therefore, TC(Q) sensitive to Q. 7. TC n ( Q ) : = h ( p n Q )/2 + RS/Q + R ( p n Q )/Q TC n + 1 ( Q )= h ( p n+1 Q )/2 + RS/Q + R ( p n+1 Q )/Q TC n + 1 ( Q )- TC n ( Q )= (p n+1 -p n )hQ /2+ R ( p n+1 -p n ) Because in all-unit discounting scheme p n+1< p n or p n+1 -p n <0, h>0, Q 0, R 0, Therefore, TC n + 1 ( Q )- TC n ( Q ) 0, TC n ( Q ) TC n + 1 ( Q ). 11. a. 2/20 net 60 means that the supplier can actually offer a payment option to the buyer where the buyer gets 2% discount if the full payment is made in 20 days or else the full amount will be due in 60 days. b. Because the discount is for full payment, this discount is an all-unit quantity discount. In my opinion this can be used as promotion scheme. If buyer known this promotion scheme, they probably order more goods which values equal or

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