X( 1, 1) 3.000000 0.000000 X( 1, 2) 3.000000 0.000000 X( 1, 3) 2.000000 0.000000 X( 1, 4) 5.000000 0.000000 X( 1, 5) 5.000000 0.000000 X( 1, 6) 2.000000 0.000000 X( 1, 7) 4.000000 0.000000 X( 1, 8) 6.056431 0.000000 X( 1, 9) 3.000000 0.000000 X( 1, 10) 4.000000 0.000000 X( 2, 1) 1.047551 0.000000 X( 2, 2) 1.376352 0.000000 X( 2, 3) 1.576097 0.000000 X( 2, 4) 2.424625 0.000000 X( 2, 5) 2.759834 0.000000 X( 2, 6) 2.815541 0.000000 X( 2, 7) 0.1236478 0.000000 X( 2, 8) 0.4424038 0.000000 X( 2, 9) 0.6322618 0.000000 X( 2, 10) 0.7452555 0.000000 方案设定：
生产方案：根据以上求解结果，公司要以最大生产力来产化肥，即是生产氮肥：5万吨；磷肥：6.5万吨；钾肥6.2万吨，销售部可得到最大利润为 160.7万元。
销售方案：（意向内）氮肥N1和N2都销售3千吨，N3销售2千吨；磷肥P1和P2都销售5千吨，P3销售2千吨；钾肥K1销售4千吨，K2销售6千吨，K3销售3千吨，K4销售4千吨。
（计划外）氮肥N1销售1千吨，N2销售1.4千吨，N3销售1.6千吨；磷肥P1销售2.4千吨，P2销售2.8千吨，P3销售2.8千吨；钾肥K1销售0.1千吨，K2销售0.4千吨，K3销售0.6千吨，K4销售0.7千吨。
3．3对问题（3）通过LINGO编程如下： sets:
w/1..3/:w1,w2; z/1..4/:; u/1..2/:t;
v/1..10/:; uw(u,w):;!2X3; uz(u,z):;!2X4;
uv(u,v):x,k1,k2,p,a1,a2,b1,b2;!2X10,,,k=ax+b;!P1i为意向，p2i为计划外。a1,b1 ,k1为公司参数；a2,b2,k2销售部参数; endsets data:
w1=12 20 19;
2
共19页
p=3 3 2 5 5 2 4 10 3 4 4 4 4 4 4 3 4 5 3 3; a1=-0.0757 -0.0827 -0.0854 -0.1984 -0.2263 -0.2319 -0.2413 -0.2582 -0.2727 -0.2792
-0.1173 -0.1341 -0.1417 -0.3263 -0.385 -0.3987 -0.4027 -0.432 -0.4651 -0.4757;
b1=0.8849 0.965 0.9985 2.3208 2.6555 2.7219 2.8072 3.0034 3.1723 3.2487
2.1392 2.3594 2.4576 5.7027 6.6587 6.8794 6.954 7.424 7.8788 8.074;
a2=-0.1112 -0.1216 -0.1259 -0.2931 -0.334 -0.3425 -0.3617 -0.3874 -0.4097 -0.4179
-0.0586 -0.064 -0.0629 -0.1533 -0.1749 -0.1792 -0.1857 -0.1986 -0.1978 -0.2031;
b2=1.9097 2.0834 2.1618 5.0214 5.7535 5.9009 6.0859 6.5175 6.8887 7.0435
0.5911 0.6445 0.6666 1.5483 1.7703 1.814 1.8709 2.0007 2.0751 2.1277;
enddata
max=t(1)+t(2);
t(1)=@sum(uv(i,j):x(i,j)*k1(i,j));
t(2)=@sum(uv(i,j):x(i,j)*k2(i,j));!意向x(1,j)*k(1,j),计划外x(2,j)*k(2,j);
@for(uv(i,j):k1(i,j)=a1(i,j)*x(i,j)+b1(i,j)); @for(uv(i,j):k2(i,j)=a2(i,j)*x(i,j)+b2(i,j));
w2(1)=@sum(uw(i,j):x(i,j));
w2(2)=@sum(uw(i,j):x(i,3+j));!k<=ax+b; w2(3)=@sum(uz(i,j):x(i,6+j));
@for(uv(i,j):x(i,j)<=p(i,j));
@sum(uw(i,j):x(i,j))<=w1(1);
@sum(uw(i,j):x(i,3+j))<=w1(2); !k<=ax+b; @sum(uz(i,j):x(i,6+j))<=w1(3); end
得到部分结果如下：
Objective value: 309.9514 Variable Value Reduced Cost X( 1, 1) 1.701974 0.000000
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共19页
X( 1, 2) 2.178164 0.000000 X( 1, 3) 2.000000 0.000000 X( 1, 4) 3.495181 0.000000 X( 1, 5) 4.017993 0.000000 X( 1, 6) 2.000000 0.000000 X( 1, 7) 1.946873 0.000000 X( 1, 8) 2.304623 0.000000 X( 1, 9) 2.576076 0.000000 X( 1, 10) 2.687584 0.000000 X( 2, 1) 1.625634 0.000000 X( 2, 2) 2.134018 0.000000 X( 2, 3) 2.360210 0.000000 X( 2, 4) 3.486826 0.000000 X( 2, 5) 4.000000 0.000000 X( 2, 6) 3.000000 0.000000 X( 2, 7) 1.937227 0.000000 X( 2, 8) 2.283166 0.000000 X( 2, 9) 2.571073 0.000000 X( 2, 10) 2.693377 0.000000 方案设定：
生产方案：根据以上求解结果，公司要以最大生产力来产化肥，即是生产氮肥：5万吨；磷肥：6.5万吨；钾肥6.2万吨，公司和销售部可得到总利润为 310.0万元。
销售方案：（意向内）氮肥N1销售1.7千吨，N2销售,2.2千吨，N3销售2千吨；磷肥P1销售3.5千吨，P2销售4千吨，P3销售2千吨；钾肥K1销售2千吨，K2销售2.3千吨，K3销售2.6千吨，K4销售2.7千吨。
（计划外）氮肥N1销售1.6千吨，N2销售2.1千吨，N3销售2.4千吨；磷肥P1销售3.5千吨，P2销售4千吨，P3销售3千吨；钾肥K1销售1.9千吨，K2销售2.3千吨，K3销售2.6千吨，K4销售2.7千吨。
3．4对问题（4）通过LINGO编程如下： sets:
w/1..3/:w1,w2; z/1..4/:; u/1..2/:t,s;
v/1..10/:; uw(u,w):;!2X3; uz(u,z):;!2X4;
uv(u,v):x,k1,k2,p,a1,a2,b1,b2,c;!2X10,,,k=ax+b;!P1i为意向，p2i为计划外。a1,b1 ,k1为公司参数；a2,b2,k2销售部参数; endsets data:
w1=12 20 19;
c=0.194029851 0.144278607 0.094527363 0.195238095 0.280952381 0.076190476 0.099502488 0.268656716 0.124378109
2
共19页
0.119402985
0.179104478 0.179104478 0.208955224 0.180952381 0.171428571 0.095238095 0.114427861 0.139303483 0.059701493 0.074626866; p=3 3 2 5 5 2 4 10 3 4 4 4 4 4 4 3 4 5 3 3; a1=-0.0757 -0.0827 -0.0854 -0.1984 -0.2263 -0.2319 -0.2413 -0.2582 -0.2727 -0.2792
-0.1173 -0.1341 -0.1417 -0.3263 -0.385 -0.3987 -0.4027 -0.432 -0.4651 -0.4757;
b1=0.8849 0.965 0.9985 2.3208 2.6555 2.7219 2.8072 3.0034 3.1723 3.2487
2.1392 2.3594 2.4576 5.7027 6.6587 6.8794 6.954 7.424 7.8788 8.074;
a2=-0.1112 -0.1216 -0.1259 -0.2931 -0.334 -0.3425 -0.3617 -0.3874 -0.4097 -0.4179
-0.0586 -0.064 -0.0629 -0.1533 -0.1749 -0.1792 -0.1857 -0.1986 -0.1978 -0.2031;
b2=1.9097 2.0834 2.1618 5.0214 5.7535 5.9009 6.0859 6.5175 6.8887 7.0435
0.5911 0.6445 0.6666 1.5483 1.7703 1.814 1.8709 2.0007 2.0751 2.1277;
enddata
max=s(1)+s(2);
s(1)=@sum(uv(i,j):x(i,j)*k1(i,j)*c(i,j)); s(2)=@sum(uv(i,j):x(i,j)*k2(i,j)*c(i,j));
t(1)=@sum(uv(i,j):x(i,j)*k1(i,j));
t(2)=@sum(uv(i,j):x(i,j)*k2(i,j));!意向x(1,j)*k(1,j),计划外x(2,j)*k(2,j);
w2(1)=@sum(uw(i,j):x(i,j));
w2(2)=@sum(uw(i,j):x(i,3+j));!k<=ax+b; w2(3)=@sum(uz(i,j):x(i,6+j));
@for(uv(i,j):x(i,j)<=p(i,j));
@sum(uw(i,j):x(i,j))<=w1(1);
@sum(uw(i,j):x(i,3+j))<=w1(2); !k<=ax+b; @sum(uz(i,j):x(i,6+j))<=w1(3);
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共19页
@for(uv(i,j):k1(i,j)<=a1(i,j)*x(i,j)+b1(i,j)); @for(uv(i,j):k2(i,j)<=a2(i,j)*x(i,j)+b2(i,j)); end
得到部分结果如下：
Objective value: 48.81505 Variable Value Reduced Cost T( 1) 123.0476 0.000000 T( 2) 148.9320 0.000000 X( 1, 1) 2.887295 0.000000 X( 1, 2) 0.000000 0.1353619 X( 1, 3) 0.000000 0.2088715 X( 1, 4) 4.329777 0.000000 X( 1, 5) 5.000000 0.000000 X( 1, 6) 0.6222572 0.000000 X( 1, 7) 2.006506 0.000000 X( 1, 8) 5.516882 0.000000 X( 1, 9) 3.000000 0.000000 X( 1, 10) 3.512998 0.000000 X( 2, 1) 2.478757 0.000000 X( 2, 2) 2.891537 0.000000 X( 2, 3) 3.742411 0.000000 X( 2, 4) 4.000000 0.000000 X( 2, 5) 4.000000 0.000000 X( 2, 6) 2.047966 0.000000 X( 2, 7) 0.000000 0.3160171 X( 2, 8) 3.806650 0.000000 X( 2, 9) 0.000000 0.4675446 X( 2, 10) 1.156964 0.000000 方案设定：
生产方案：根据以上求解结果，公司要以最大生产力来产化肥，即是生产氮肥：5万吨；磷肥：6.5万吨；钾肥6.2万吨。公司和销售部总利润为272.0万元。
销售方案：（意向内）氮肥N1销售2.9千吨，N2和N3都不销售；磷肥P1销售4.3千吨，P2销售5千吨，P3销售0.6千吨；钾肥K1销售2千吨，K2销售5.5千吨，K3销售3千吨，K4销售3.5千吨。
（计划外）氮肥N1销售2.5千吨，N2销售2.9千吨，N3销售3.7千吨；磷肥P1销售4千吨，P2销售4千吨，P3销售2千吨；钾肥K1销售0千吨，K2销售3.8千吨，K3销售0千吨，K4销售1.2千吨。
3．5对问题（5）通过LINGO编程如下： sets:
w/1..3/:w1,w2; z/1..4/:t; u/1..2/:;
2
共19页
农业化肥公司的生产与销售问题论文
