x23*(1+0.0325)+x14*(1+2*0.0375)+y21*(1+0.037)=m3; x33+x34+x35+x36+y31+y32+y33=n3; m3-a=n3;
x33*(1+0.0325)+x24*(1+2*0.0375)+x15*(1+3*0.0425)+y31*(1+0.037)+y12*(1+3*0.0543)=m4;
x43+x44+x45+x46+y41+y42+y43=n4; m4-a=n4;
x43*(1+0.0325)+x34*(1+2*0.0375)+x25*(1+3*0.0425)+y41*(1+0.037)+y22*(1+3*0.0543)=m5;
x53+x54+x55+x56+y51+y52+y53=n5; m5-a=n5;
x53*(1+0.0325)+x44*(1+2*0.0375)+x35*(1+3*0.0425)+x16*(1+5*0.0475)+y51*(1+0.037)+y32*(1+3*0.0543)+y13*(1+5*0.06)=m6; x63+x64+x65+x66+y61+y62+y63=n6; m6-a=n6;
x63*(1+0.0325)+x54*(1+2*0.0375)+x45*(1+3*0.0425)+x26*(1+5*0.0475)+y61*(1+0.037)+y42*(1+3*0.0543)+y23*(1+5*0.06)=m7; x73+x74+x75+y71+y72=n7; m7-a=n7;
x73*(1+0.0325)+x64*(1+2*0.0375)+x55*(1+3*0.0425)+x36*(1+5*0.0475)+y71*(1+0.037)+y52*(1+3*0.0543)+y33*(1+5*0.06)=m8; x83+x84+x85+y81+y82=n8; m8-a=n8;
x83*(1+0.0325)+x74*(1+2*0.0375)+x65*(1+3*0.0425)+x46*(1+5*0.0475)+y81*(1+0.037)+y62*(1+3*0.0543)+y43*(1+5*0.06)=m9; x93+x94+y91=n9; m9-a=n9;
x93*(1+0.0325)+x84*(1+2*0.0375)+x75*(1+3*0.0425)+x56*(1+5*0.0475)+y91*(1+0.037)+y72*(1+3*0.0543)+y53*(1+5*0.06)=m10; x103+y101=n10; m10-a=n10;
x103*(1+0.0325)+x94*(1+2*0.0375)+x85*(1+3*0.0425)+x66*(1+5*0.0475)+y101*(1+0.037)+y82*(1+3*0.0543)+y63*(1+5*0.06)=m11; m11-a=m1; @gin (56);
采用活期、半年期、国库券的“组合式”投资模型Ⅲ：
max=a; m1=3000;
x13+x14+x15+x16+y11+y12+y13=n1; m1=n1;
x13*(1+0.0325)=m2;
x23+x24+x25+x26+y21+y22+y23=n2; m2-a=n2;
x23*(1+0.0325)+x14*(1+2*0.0375)+y11*1.0557=m3;
15
x33+x34+x35+x36+y31+y32+y33=n3; m3-a=n3;
x33*(1+0.0325)+x24*(1+2*0.0375)+x15*(1+3*0.0425)+y21*1.0557=m4; x43+x44+x45+x46+y41+y42+y43=n4; m4-a=n4;
x43*(1+0.0325)+x34*(1+2*0.0375)+x25*(1+3*0.0425)+y31*1.0557+y12*1.1839=m5; x53+x54+x55+x56+y51+y52+y53=n5; m5-a=n5;
x53*(1+0.0325)+x44*(1+2*0.0375)+x35*(1+3*0.0425)+x16*(1+5*0.0475)+y41*1.0557+y22*1.1839=m6;
x63+x64+x65+x66+y61+y62+y63=n6; m6-a=n6;
x63*(1+0.0325)+x54*(1+2*0.0375)+x45*(1+3*0.0425)+x26*(1+5*0.0475)+y51*1.0557+y32*1.1839+y13*1.3234=m7; x73+x74+x75+y71+y72=n7; m7-a=n7;
x73*(1+0.0325)+x64*(1+2*0.0375)+x55*(1+3*0.0425)+x36*(1+5*0.0475)+y61*1.0557+y42*1.1839+y23*1.3234=m8; x83+x84+x85+y81+y82=n8; m8-a=n8;
x83*(1+0.0325)+x74*(1+2*0.0375)+x65*(1+3*0.0425)+x46*(1+5*0.0475)+y71*1.0557+y52*1.1839+y33*1.3234=m9; x93+x94+y91=n9; m9-a=n9;
x93*(1+0.0325)+x84*(1+2*0.0375)+x75*(1+3*0.0425)+x56*(1+5*0.0475)+y81*1.0557+y62*1.1839+y43*1.3234=m10; x103+y101=n10; m10-a=n10;
x103*(1+0.0325)+x94*(1+2*0.0375)+x85*(1+3*0.0425)+x66*(1+5*0.0475)+y91*1.0557+y72*1.1839+y53*1.3234=m11; m11-a=m1; @gin (56);
采用半年期、国库券的“组合式”投资模型Ⅳ：
max=a; m1=3000;
x13+x14+x15+x16+y11+y12+y13=n1; m1=n1;
x13*(1+0.0325)=m2;
x23+x24+x25+x26+y21+y22+y23=n2; m2-a=n2;
x23*(1+0.0325)+x14*(1+2*0.0375)+y11*1.0686=m3; x33+x34+x35+x36+y31+y32+y33=n3; m3-a=n3;
x33*(1+0.0325)+x24*(1+2*0.0375)+x15*(1+3*0.0425)+y21*1.0686=m4;
16
x43+x44+x45+x46+y41+y42+y43=n4; m4-a=n4;
x43*(1+0.0325)+x34*(1+2*0.0375)+x25*(1+3*0.0425)+y31*1.0686+y12*1.1984=m5; x53+x54+x55+x56+y51+y52+y53=n5; m5-a=n5;
x53*(1+0.0325)+x44*(1+2*0.0375)+x35*(1+3*0.0425)+x16*(1+5*0.0475)+y41*1.0686+y22*1.1984=m6;
x63+x64+x65+x66+y61+y62+y63=n6; m6-a=n6;
x63*(1+0.0325)+x54*(1+2*0.0375)+x45*(1+3*0.0425)+x26*(1+5*0.0475)+y51*1.0686+y32*1.1984+y13*1.3397=m7; x73+x74+x75+y71+y72=n7; m7-a=n7;
x73*(1+0.0325)+x64*(1+2*0.0375)+x55*(1+3*0.0425)+x36*(1+5*0.0475)+y61*1.0686+y42*1.1984+y23*1.3397=m8; x83+x84+x85+y81+y82=n8; m8-a=n8;
x83*(1+0.0325)+x74*(1+2*0.0375)+x65*(1+3*0.0425)+x46*(1+5*0.0475)+y71*1.0686+y52*1.1984+y33*1.3397=m9; x93+x94+y91=n9; m9-a=n9;
x93*(1+0.0325)+x84*(1+2*0.0375)+x75*(1+3*0.0425)+x56*(1+5*0.0475)+y81*1.0686+y62*1.1984+y43*1.3397=m10; x103+y101=n10; m10-a=n10;
x103*(1+0.0325)+x94*(1+2*0.0375)+x85*(1+3*0.0425)+x66*(1+5*0.0475)+y91*1.0686+y72*1.1984+y53*1.3397=m11; m11-a=m1; @gin (56);
附录3：求解问题三的LINGO程序
用模型Ⅱ解题： max=a; m1=3000;
x13+x14+x15+x16+y11+y12+y13=n1; m1=n1;
x13*(1+0.0325)+y11*(1+0.037)=m2; x23+x24+x25+x26+y21+y22+y23=n2; m2-a=n2;
x23*(1+0.0325)+x14*(1+2*0.0375)+y21*(1+0.037)=m3; x33+x34+x35+x36+y31+y32+y33=n3; m3-a=n3;
x33*(1+0.0325)+x24*(1+2*0.0375)+x15*(1+3*0.0425)+y31*(1+0.037)+y12*(1+3*0.0543)=m4;
x43+x44+x45+x46+y41+y42+y43=n4;
17
m4-a=n4;
x43*(1+0.0325)+x34*(1+2*0.0375)+x25*(1+3*0.0425)+y41*(1+0.037)+y22*(1+3*0.0543)=m5;
x53+x54+x55+x56+y51+y52+y53=n5; m5-a=n5;
x53*(1+0.0325)+x44*(1+2*0.0375)+x35*(1+3*0.0425)+x16*(1+5*0.0475)+y51*(1+0.037)+y32*(1+3*0.0543)+y13*(1+5*0.06)=m6; x63+x64+x65+x66+y61+y62+y63=n6; m6-a=n6;
x63*(1+0.0325)+x54*(1+2*0.0375)+x45*(1+3*0.0425)+x26*(1+5*0.0475)+y61*(1+0.037)+y42*(1+3*0.0543)+y23*(1+5*0.06)=m7; x73+x74+x75+y71+y72=n7; m7-a=n7;
x73*(1+0.0325)+x64*(1+2*0.0375)+x55*(1+3*0.0425)+x36*(1+5*0.0475)+y71*(1+0.037)+y52*(1+3*0.0543)+y33*(1+5*0.06)=m8; x83+x84+x85+y81+y82=n8; m8-1.2*a=n8;
x83*(1+0.0325)+x74*(1+2*0.0375)+x65*(1+3*0.0425)+x46*(1+5*0.0475)+y81*(1+0.037)+y62*(1+3*0.0543)+y43*(1+5*0.06)=m9; x93+x94+y91=n9; m9-a=n9;
x93*(1+0.0325)+x84*(1+2*0.0375)+x75*(1+3*0.0425)+x56*(1+5*0.0475)+y91*(1+0.037)+y72*(1+3*0.0543)+y53*(1+5*0.06)=m10; x103+y101=n10; m10-a=n10;
x103*(1+0.0325)+x94*(1+2*0.0375)+x85*(1+3*0.0425)+x66*(1+5*0.0475)+y101*(1+0.037)+y82*(1+3*0.0543)+y63*(1+5*0.06)=m11; m11-a=m1;
用模型Ⅲ解题：
max=a; m1=3000;
x13+x14+x15+x16+y11+y12+y13=n1; m1=n1;
x13*(1+0.0325)=m2;
x23+x24+x25+x26+y21+y22+y23=n2; m2-a=n2;
x23*(1+0.0325)+x14*(1+2*0.0375)+y11*1.0557=m3; x33+x34+x35+x36+y31+y32+y33=n3; m3-a=n3;
x33*(1+0.0325)+x24*(1+2*0.0375)+x15*(1+3*0.0425)+y21*1.0557=m4; x43+x44+x45+x46+y41+y42+y43=n4; m4-a=n4;
x43*(1+0.0325)+x34*(1+2*0.0375)+x25*(1+3*0.0425)+y31*1.0557+y12*1.1839=m5; x53+x54+x55+x56+y51+y52+y53=n5;
18
m5-a=n5;
x53*(1+0.0325)+x44*(1+2*0.0375)+x35*(1+3*0.0425)+x16*(1+5*0.0475)+y41*1.0557+y22*1.1839=m6;
x63+x64+x65+x66+y61+y62+y63=n6; m6-a=n6;
x63*(1+0.0325)+x54*(1+2*0.0375)+x45*(1+3*0.0425)+x26*(1+5*0.0475)+y51*1.0557+y32*1.1839+y13*1.3234=m7; x73+x74+x75+y71+y72=n7; m7-a=n7;
x73*(1+0.0325)+x64*(1+2*0.0375)+x55*(1+3*0.0425)+x36*(1+5*0.0475)+y61*1.0557+y42*1.1839+y23*1.3234=m8; x83+x84+x85+y81+y82=n8; m8-1.2*a=n8;
x83*(1+0.0325)+x74*(1+2*0.0375)+x65*(1+3*0.0425)+x46*(1+5*0.0475)+y71*1.0557+y52*1.1839+y33*1.3234=m9; x93+x94+y91=n9; m9-a=n9;
x93*(1+0.0325)+x84*(1+2*0.0375)+x75*(1+3*0.0425)+x56*(1+5*0.0475)+y81*1.0557+y62*1.1839+y43*1.3234=m10; x103+y101=n10; m10-a=n10;
x103*(1+0.0325)+x94*(1+2*0.0375)+x85*(1+3*0.0425)+x66*(1+5*0.0475)+y91*1.0557+y72*1.1839+y53*1.3234=m11; m11-a=m1; @gin (56);
用模型Ⅳ解题：
max=a; m1=3000;
x13+x14+x15+x16+y11+y12+y13=n1; m1=n1;
x13*(1+0.0325)=m2;
x23+x24+x25+x26+y21+y22+y23=n2; m2-a=n2;
x23*(1+0.0325)+x14*(1+2*0.0375)+y11*1.0686=m3; x33+x34+x35+x36+y31+y32+y33=n3; m3-a=n3;
x33*(1+0.0325)+x24*(1+2*0.0375)+x15*(1+3*0.0425)+y21*1.0686=m4; x43+x44+x45+x46+y41+y42+y43=n4; m4-a=n4;
x43*(1+0.0325)+x34*(1+2*0.0375)+x25*(1+3*0.0425)+y31*1.0686+y12*1.1984=m5; x53+x54+x55+x56+y51+y52+y53=n5; m5-a=n5;
x53*(1+0.0325)+x44*(1+2*0.0375)+x35*(1+3*0.0425)+x16*(1+5*0.0475)+y41*1.0686+y22*1.1984=m6;
19
x63+x64+x65+x66+y61+y62+y63=n6; m6-a=n6;
x63*(1+0.0325)+x54*(1+2*0.0375)+x45*(1+3*0.0425)+x26*(1+5*0.0475)+y51*1.0686+y32*1.1984+y13*1.3397=m7; x73+x74+x75+y71+y72=n7; m7-a=n7;
x73*(1+0.0325)+x64*(1+2*0.0375)+x55*(1+3*0.0425)+x36*(1+5*0.0475)+y61*1.0686+y42*1.1984+y23*1.3397=m8; x83+x84+x85+y81+y82=n8; m8-1.2*a=n8;
x83*(1+0.0325)+x74*(1+2*0.0375)+x65*(1+3*0.0425)+x46*(1+5*0.0475)+y71*1.0686+y52*1.1984+y33*1.3397=m9; x93+x94+y91=n9; m9-a=n9;
x93*(1+0.0325)+x84*(1+2*0.0375)+x75*(1+3*0.0425)+x56*(1+5*0.0475)+y81*1.0686+y62*1.1984+y43*1.3397=m10; x103+y101=n10; m10-a=n10;
x103*(1+0.0325)+x94*(1+2*0.0375)+x85*(1+3*0.0425)+x66*(1+5*0.0475)+y91*1.0686+y72*1.1984+y53*1.3397=m11; m11-a=m1; @gin (56);
20