min=0.6*Z31+0.4*Z32;
Z31=(P12+0.53961) 2+(P22+0.33515) 2+(P32+0.01741) 2+(P42-0.176133) 2+(P52-0.182692) 2
+(P62-0.285535) 2+(P72-0.269575) 2+(P82-0.130416) 2+(P92-0.155665) 2+(P102-0.181702) 2
+(P112-0.138873) 2+(P122+0.01682) 2+(P132+0.00069) 2+(P142-0.066818) 2;
Z32=(P143-P141) 2+(P133-P131) 2+(P123-P121) 2+(P113-P111) 2+(P103-P101) 2+(P93-P91)2
+(P83-P81) 2+(P73-P71)2+(P63-P61) 2+(P53-P51) 2+(P43-P41) 2+(P33-P31) 2
+(P23-P21) 2+(P13-P11) 2;
P11+0.15*P12-0.15*P11<=-0.53961;
P21+0.15*P22-0.15*P21<=-0.33515;
P31+0.15*P32-0.15*P31<=-0.01741;
P41+0.15*P42-0.15*P41<=0.176133;
P51+0.15*P52-0.15*P51<=0.182692;
P61+0.15*P62-0.15*P61<=0.285535;
P71+0.15*P72-0.15*P71<=0.269575;
P81+0.15*P82-0.15*P81<=0.130416;
P91+0.15*P92-0.15*P91<=0.155665;
P101+0.15*P102-0.15*P101<=0.181702;
P111+0.15*P112-0.15*P111<=0.138873;
P121+0.15*P122-0.15*P121<=-0.01682;
P131+0.15*P132-0.15*P131<=-0.00069;
P141+0.15*P142-0.15*P141<=0.066818;
P13+0.15*P12-0.15*P13>=-0.53961;
P23+0.15*P22-0.15*P23>=-0.33515;
P33+0.15*P32-0.15*P33>=-0.01741;
P43+0.15*P42-0.15*P43>=0.176133;
P53+0.15*P52-0.15*P53>=0.182692;
P63+0.15*P62-0.15*P63>=0.285535;
P73+0.15*P72-0.15*P73>=0.269575;
P83+0.15*P82-0.15*P83>=0.130416;
P93+0.15*P92-0.15*P93>=0.155665;
P103+0.15*P102-0.15*P103>=0.181702;
P113+0.15*P112-0.15*P113>=0.138873;
P123+0.15*P122-0.15*P123>=-0.01682;
P133+0.15*P132-0.15*P133>=-0.00069;
P143+0.15*P142-0.15*P143>=0.066818;
P11=a1-b3/1;
P21=a1-b3/2;
P31=a1-b3/3;
P41=a1-b3/4;
P51=a1-b3/5;
P61=a1-b3/6;
P71=a1-b3/7;
P81=a1-b3/8;
P91=a1-b3/9;
P101=a1-b3/10;
P111=a1-b3/11;
P121=a1-b3/12;
P131=a1-b3/13;
P141=a1-b3/14;
P12=a2-b2/1;
P22=a2-b2/2;
P32=a2-b2/3;
P42=a2-b2/4;
P52=a2-b2/5;
P62=a2-b2/6;
P72=a2-b2/7;
P82=a2-b2/8;
P92=a2-b2/9;
P102=a2-b2/10;
P112=a2-b2/11;
P122=a2-b2/12;
P132=a2-b2/13;
P142=a2-b2/14;
P13=a3-b1/1;
P23=a3-b1/2;
P33=a3-b1/3;
P43=a3-b1/4;
P53=a3-b1/5;
P63=a3-b1/6;
P73=a3-b1/7;
P83=a3-b1/8;
P93=a3-b1/9;
P103=a3-b1/10;
P113=a3-b1/11;
P123=a3-b1/12;
P133=a3-b1/13;
P143=a3-b1/14;
a1>=0;
a2>=a1;
a3>=a2;
b1>=0;
b2>=b1;
b3>=b2;
@free(P11);@free(P12);@free(P13);@free(P21);@free(P22);@free(P23);@free(P31);@free(P32);
@free(P33);@free(P41);@free(P42);@free(P43);@free(P51);@free(P52);@free(P53); @free(P61);
@free(P62);@free(P63);@free(P71);@free(P72);@free(P73);@free(P81);@free(P82);@free(P83);
@free(P91);@free(P92);@free(P93);@free(P101);@free(P102);@free(P103);@free(P111);
@free(P112); @free(P113);@free(P121);@free(P122);@free(P123);@free(P131);
@free(P132);@free(P133);@free(P141);@free(P142);@free(P143);
Algorithm 1: The linear programming problem (coded using Lingo).