C11 70.00000 C12 57.00000 C13 42.00000 C14 24.00000
Row Slack or Surplus 1 0.9667117 2 54.99845 3 0.1550597E-02 4 9.996899 5 20.00000 6 25.00000 7 30.00000 8 35.00000 9 40.00000 10 40.00000 11 45.00000 12 50.00000 13 55.00000 14 60.00000 15 65.00000 16 75.00000 17 90.00000 18 100.0000 19 0.000000 20 0.000000 21 0.000000 22 0.000000 23 0.000000 24 0.000000 25 0.000000 26 0.000000 27 0.000000 28 0.000000 29 0.000000 30 0.000000 31 0.000000 32 0.000000 33 0.000000 34 0.000000 35 0.000000 36 0.000000
37 0.000000 38 0.000000 39 0.000000 40 0.000000 41 0.000000 42 0.000000 43 0.000000 44 0.000000 45 0.000000 46 0.000000
根据lingo求解结果可知： 最优解的利用率比值96.67％ 外接圆公差带为: 650?760
铁心柱截面积的公差带为:
639 ?747
附录五：
max=x1*y1+2*x2*y2+2*x3*y3+2*x4*y4+2*x5*y5+2*x6*y6+2*x7*y7+2*x8*y8+2*x9*y9+2*x10*y10+2*x11*y11+2*x12*y12+2*x13*y13+2*x14*y14; x1<=650; x1>=x2; x2>=x3; x3>=x4; x4>=x5; x5>=x6; x6>=x7; x7>=x8; x8>=x9; x9>=x10; x10>=x11; x11>=x12; x12>=x13; x13>=x14; x14>=20; x1/5=c1; x2/5=c2; x3/5=c3; x4/5=c4; x5/5=c5; x6/5=c6;
x7/5=c7; x8/5=c8; x9/5=c9; x10/5=c10; x11/5=c11; x12/5=c12; x13/5=c13; x14/5=c14; @gin(c1); @gin(c2); @gin(c3); @gin(c4); @gin(c5); @gin(c6); @gin(c7); @gin(c8); @gin(c9); @gin(c10); @gin(c11); @gin(c12); @gin(c13); @gin(c14);
(x1/2)*(x1/2)+(y1/2)*(y1/2)=325*325;
(x2/2)*(x2/2)+(y1/2+y2)*(y1/2+y2)=325*325;
(x3/2)*(x3/2)+(y1/2+y2+y3)*(y1/2+y2+y3)=325*325;
(x4/2)*(x4/2)+(y1/2+y2+y3+y4)*(y1/2+y2+y3+y4)=325*325;
(x5/2)*(x5/2)+(y1/2+y2+y3+y4+y5)*(y1/2+y2+y3+y4+y5)=325*325;
(x6/2)*(x6/2)+(y1/2+y2+y3+y4+y5+y6)*(y1/2+y2+y3+y4+y5+y6)=325*325;
(x7/2)*(x7/2)+(y1/2+y2+y3+y4+y5+y6+y7)*(y1/2+y2+y3+y4+y5+y6+y7)=325*325; (x8/2)*(x8/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8)*(y1/2+y2+y3+y4+y5+y6+y7+y8)=325*325; (x9/2)*(x9/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8+y9)*(y1/2+y2+y3+y4+y5+y6+y7+y8+y9)=325*325;
(x10/2)*(x10/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10)*(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10)=325*325;
(x11/2)*(x11/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11)*(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11)=325*325;
(x12/2)*(x12/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12)*(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12)=325*325;
(x13/2)*(x13/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13)*(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13)=325*325;
(x14/2)*(x14/2)+(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13+y14)*(y1/2+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13+y14)=325*325;
h1=y1+y2+y3+y3+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13+y14;
s1=x1*y1;
s2=x2*y2;
s3=x3*y3;
s4=x4*y4;
s5=x5*y5;
s6=x6*y6;
s7=x7*y7;
s8=x8*y8;
s9=x9*y9;
s10=x10*y10;
s11=x11*y11;
s12=x12*y12;
s13=x13*y13;
s14=x14*y14;
所求的的结果为：
一二级中间，一级面积 ：72690.048
五六级中间， 2到5级 面积： 66819.92 七到十四级，剩余面积: 57169
Local optimal solution found.
Objective value: Objective bound: Infeasibilities: Extended solver steps: Total solver iterations:
Variable X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X10 Y10 X11 Y11 X12 Y12 X13 320668.4 320668.4 0.8069389E-01 247 67566 Value Reduced Cost 640.0000 0.000000 113.5796 0.000000 625.0000 0.000000 32.47806 0.000000 605.0000 0.000000 29.55449 0.000000 580.0000 0.000000 27.89166 0.000000 555.0000 0.000000 22.45676 0.000000 520.0000 0.000000 25.82923 0.000000 485.0000 0.000000 21.37641 0.000000 445.0000 0.000000 20.51756 0.000000 395.0000 0.000000 21.21212 0.000000 345.0000 0.000000 17.33674 0.000000 290.0000 0.000000 15.41797 0.000000 230.0000 0.000000 13.11289 0.000000 165.0000 0.000000