专题3-4 插值与拟合+数值微分积分(6)

OBJECTIVE FUNCTION VALUE

1) 632.2581

VARIABLE VALUE REDUCED COST X1 64.516129 0.000000 X2 167.741928 0.000000 X3 0.000000 0.946237

ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 0.731183 3) 0.000000 0.003226

NO. ITERATIONS= 0

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 2.000000 1.360000 0.500000 X2 3.000000 1.000000 0.550000 X3 4.000000 0.946237 INFINITY

RIGHTHAND SIDE RANGES

ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 600.000000 119.999992 278.571411 3 60000.000000 52000.000000 10000.000000 程序5：model:

Max=4.8*x11+4.8*x21+5.6*x12+5.6*x22-10*x1-8*x2-6*x3; x11+x120; 0.4*x12-0.6*x22>0; x=x1+x2+x3; (x1-500)*x2=0; (x2-500)*x3=0; x1<500; x2<500; x3<500;

x>0; x11>0; x12>0; x21>0; x22>0; x1>0; x2>0; x3>0; end

Rows= 19 Vars= 8 No. integer vars= 0

Nonlinear rows= 2 Nonlinear vars= 3 Nonlinear constraints= 2

Nonzeros= 42 Constraint nonz= 28 Density=0.246

No. < : 5 No. =: 3 No. > : 10, Obj=MAX Single cols= 0

Optimal solution found at step: 4 Objective value: 4800.000

Variable Value Reduced Cost X11 500.0000 0.0000000 X21 500.0000 0.0000000 X12 0.0000000 0.0000000 X22 0.0000000 0.0000000 X1 0.1021405E-13 10.00000 X2 0.0000000 8.000000 X3 0.0000000 6.000000 X 0.0000000 0.0000000

Row Slack or Surplus Dual Price 1 4800.000 1.000000 2 0.0000000 9.600000 3 500.0000 0.0000000 4 0.0000000 -9.600000 5 0.0000000 -9.333333 6 0.0000000 0.0000000 7 0.0000000 0.0000000 8 0.0000000 0.0000000 9 500.0000 0.0000000 10 500.0000 0.0000000 11 500.0000 0.0000000 12 0.0000000 9.600000 13 500.0000 0.0000000

14 0.0000000 -0.2666667 15 500.0000 0.0000000 16 0.0000000 0.0000000 17 0.0000000 0.0000000 18 0.0000000 0.0000000 19 0.0000000 0.0000000

程序6：max 4.8x11+4.8x21+5.6x12+5.6x22-10x1-8x2-6x3 st

x-x1-x2-x3=0 x11+x12-x<500 x21+x22<1000 0.5x11-0.5x21>0 0.4x12-0.6x22>0 x1-500y1<0 x2-500y2<0 x3-500y3<0 x1-500y2>0 x2-500y3>0 end int y1 int y2 int y3

ENUMERATION COMPLETE. BRANCHES= 2 PIVOTS=

LAST INTEGER SOLUTION IS THE BEST FOUND RE-INSTALLING BEST SOLUTION...

OBJECTIVE FUNCTION VALUE

1) 5000.000

VARIABLE VALUE REDUCED COST Y1 1.000000 0.000000 Y2 1.000000 2000.000000 Y3 1.000000 1000.000000 X11 0.000000 1.200000 X21 0.000000 0.200000 X12 1500.000000 0.000000 X22 1000.000000 0.000000 X1 500.000000 0.000000 X2 500.000000 0.000000 X3 0.000000 0.000000

28 X 1000.000000 0.000000

ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 6.000000 3) 0.000000 6.000000 4) 0.000000 5.000000 5) 0.000000 0.000000 6) 0.000000 -1.000000 7) 0.000000 0.000000 8) 0.000000 0.000000 9) 500.000000 0.000000 10) 0.000000 -4.000000 11) 0.000000 -2.000000

NO. ITERATIONS= 35

BRANCHES= 2 DETERM.= 1.000E 0

程序7：

Min 3x1+x2+3x3+3x4+x5+x6+3x7 s.t.

4x1+3x2+2x3+x4+x5>=50 x2+2x4+x5+3x6>=20 x3+x5+2x7>=15 end gin7

LP OPTIMUM FOUND AT STEP 4

OBJECTIVE FUNCTION VALUE

1) 26.66667

VARIABLE VALUE REDUCED COST X1 0.000000 1.666667 X2 11.666667 0.000000 X3 0.000000 1.666667 X4 0.000000 2.666667 X5 15.000000 0.000000 X6 0.000000 1.000000 X7 0.000000 1.666667

ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 -0.333333 3) 6.666667 0.000000

4) 0.000000 -0.666667

NO. ITERATIONS= 4

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE X1 3.000000 INFINITY 1.666667 X2 1.000000 1.250000 1.000000 X3 3.000000 INFINITY 1.666667 X4 3.000000 INFINITY 2.666667 X5 1.000000 0.833333 0.666667 X6 1.000000 INFINITY 1.000000 X7 3.000000 INFINITY 1.666667

RIGHTHAND SIDE RANGES

ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 50.000000 INFINITY 19.999998 3 20.000000 6.666667 INFINITY 4 15.000000 35.000000 9.999999

Model:

min=x1+x2+x3;

x1*r11+x2*r12+x3*r13>=50; x1*r21+x2*r22+x3*r23>=10; x1*r31+x2*r32+x3*r33>=20; x1*r41+x2*r42+x3*r43>=15; 4*r11+5*r21+6*r31+8*r41<=19; 4*r12+5*r22+6*r32+8*r42<=19; 4*r13+5*r23+6*r33+8*r43<=19; 4*r11+5*r21+6*r31+8*r41>=16; 4*r12+5*r22+6*r32+8*r42>=16; 4*r13+5*r23+6*r33+8*r43>=16; x1+x2+x3>=26; x1+x2+x3<=31; x1>=x2; x2>=x3;

@gin(x1);@gin(x2);@gin(x3); @gin(r11);@gin(r12);@gin(r13); @gin(r21);@gin(r22);@gin(r23); @gin(r31);@gin(r32);@gin(r33);

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