铁心柱截面积的公差带为:
639 ?747
在所得出的计算结果对于实际的生产加工均有借鉴意义，希望对于实际的生产有所帮助。
参考文献：
1.张杰 周硕.
运筹学模型与实验 中国电力出版社 2007
附录一：
对于级数为12：
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; 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>=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;
@gin(c1); @gin(c2); @gin(c3); @gin(c4); @gin(c5); @gin(c6); @gin(c7); @gin(c8); @gin(c9); @gin(c10); @gin(c11); @gin(c12);
(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;
h1=y1+y2+y3+y3+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12;
求解结果为：
Local optimal solution found.
Objective value: 318924.4 Objective bound: 318924.4 Infeasibilities: 0.2400483E-01 Extended solver steps: 89 Total solver iterations: 21852
Variable Value Reduced Cost X1 640.0000 0.000000 Y1 113.5786 0.000000 X2 620.0000 0.000000 Y2 40.80681 0.000000 X3 595.0000 0.000000 Y3 33.24253 0.000000 X4 565.0000 0.000000 Y4 29.84350 0.000000 X5 530.0000 0.000000 Y5 27.46674 0.000000 X6 490.0000 0.000000 Y6 25.39269 0.000000 X7 445.0000 0.000000
Y7 23.35240 0.000000 X8 395.0000 0.000000 Y8 21.21212 0.000000 X9 340.0000 0.000000 Y9 18.88670 0.000000 X10 280.0000 0.000000 Y10 16.30741 0.000000 X11 210.0000 0.000000 Y11 14.27094 0.000000 X12 120.0000 Y12 11.84240 C1 128.0000 C2 124.0000 C3 119.0000 C4 113.0000 C5 106.0000 C6 98.00000 C7 89.00000 C8 79.00000 C9 68.00000 C10 56.00000 C11 42.00000 C12 24.00000 H1 442.6879 Row Slack or Surplus 1 318924.4 2 10.00000 3 20.00000 4 25.00000 5 30.00000 6 35.00000 7 40.00000 8 45.00000 9 50.00000 10 55.00000 11 60.00000 12 70.00000 13 90.00000 14 100.0000 15 0.000000 16 0.000000 17 0.000000 18 0.000000 0.000000 0.000000 -4.402540 -11.02568 8.643625 9.237668 7.024447 4.219587 1.285712 -1.694148 -4.746646 3.990254 10.91358 -5.717395 0.000000 Dual Price 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 4.402540 11.02568 -8.643625 -9.237668
19 0.000000 -7.024447 20 0.000000 -4.219587 21 0.000000 -1.285712 22 0.000000 1.694148 23 0.000000 4.746646 24 0.000000 -3.990254 25 0.000000 -10.91358 26 0.000000 5.717395 27 -0.2400483E-01 0.3521803 28 0.000000 0.2561577 29 0.000000 0.2292901 30 0.000000 0.2178213 31 0.000000 0.2125976 32 0.000000 0.2107318 33 0.000000 0.2110649 34 0.000000 0.2130907 35 0.000000 0.2166121 36 0.000000 0.2386633 37 0.000000 0.2926152 38 0.000000 0.3756885 39 0.000000 0.000000 附录二：
针对级数13：
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; 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>=20; x1/5=c1; x2/5=c2; x3/5=c3; x4/5=c4; x5/5=c5;