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1. a. TC(2Q∗)=(R/2Q∗)S + (2Q∗/2)hC=(R/2Q∗)S + (Q∗)hCTC(Q∗)=(R/Q∗)S + (Q∗/2)hCQ∗ = EOQ, therefore, (R/Q∗)S=(Q∗/2)hCTC(2Q∗)/TC(Q∗)=((R/2Q∗)S + (Q∗)hC) /( (R/Q∗)S+(Q∗/2)hC)=5/4b. TC(Q∗/2)= (R/(Q∗/2))S + ((Q∗/2)/2)hC=(2R/Q∗)S + (Q∗/4)hCTC(Q∗/2)/TC(Q∗)=((2R/Q∗)S + (Q∗/4)hC) / ((R/Q∗)S + (Q∗/2)hC)=5/4c. Whenever Q is increase or decrease, TC(Q) all increase. Therefore, TC(Q)sensitive to Q.7. TCn(Q) :=h(pnQ)/2 +RS/Q +R(pnQ)/Q TCn+1(Q)=h(pn+1Q)/2 +RS/Q +R(pn+1Q)/Q TCn+1(Q)-TCn(Q)=(pn+1-pn)hQ/2+R(pn+1-pn)Because in all-unit discounting scheme pn+1<pn or pn+1-pn <0, h>0, Q≥0, R≥0,Therefore,TCn+1(Q)-TCn(Q)≤0,TCn(Q) ≥ TCn+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 20days or else the full amount will bedue 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