专题3-4 插值与拟合+数值微分积分(7)

@gin(r41);@gin(r42);@gin(r43); end

Rows= 15 Vars= 15 No. integer vars= 15

Nonlinear rows= 4 Nonlinear vars= 15 Nonlinear constraints= 4

Nonzeros= 73 Constraint nonz= 58 Density=0.304

No. < : 4 No. =: 0 No. > : 10, Obj=MIN Single cols= 0

Optimal solution found at step: 28970 Objective value: 28.00000 Branch count: 2946

Variable Value Reduced Cost X1 10.00000 0.0000000 X2 10.00000 0.0000000 X3 8.000000 0.0000000 R11 3.000000 0.0000000 R12 2.000000 0.0000000 R13 0.0000000 0.0000000 R21 0.0000000 0.0000000 R22 1.000000 0.0000000 R23 0.0000000 0.0000000 R31 1.000000 0.0000000 R32 1.000000 0.0000000 R33 0.0000000 0.0000000 R41 0.0000000 0.0000000 R42 0.0000000 0.0000000 R43 2.000000 0.0000000

Row Slack or Surplus Dual Price 1 28.00000 0.0000000 2 0.0000000 0.0000000 3 0.0000000 0.0000000 4 0.0000000 0.0000000 5 1.000000 0.0000000 6 1.000000 0.0000000 7 0.0000000 0.0000000 8 3.000000 0.0000000 9 2.000000 0.0000000 10 3.000000 0.0000000 11 0.0000000 0.0000000 12 2.000000 0.0000000 13 3.000000 0.0000000

14 0.0000000 0.0000000 15 2.000000 0.0000000 程序8：

Max 0.1y1-0.2226x1+0.1833x2+0.2618x3+0.1695x4+0.1571y2+0.0196y3 st

1.5x1+2x2+x3+3x4<=14.4 x1+x2+x3<=5 x4<=2

y2-x1-2x2-4x4+y1=0

y3-10x1-4x2-16x3-5x4+2y1=0 y1-x1-2x2-4x4<=0

y1-5x1+2x2+8x3+2.5x4<=0 end

ROW SLACK OR SURPLUS DUAL PRICES

2) 0.000000 0.241577 3) 0.284615 0.000000 4) 0.000000 0.055237 5) 0.000000 0.157100 6) 0.000000 0.019600 7) 15.369231 0.000000 8) 0.000000 0.046373

NO. ITERATIONS= 3

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE Y1 -0.100000 0.342673 INFINITY X1 -0.222600 0.034507 1.570250 X2 0.183300 0.038297 0.028418 X3 0.261800 0.037162 INFINITY X4 0.169500 INFINITY 0.055237 Y2 0.157100 INFINITY 0.024155 Y3 0.019600 0.001725 0.078512

RIGHTHAND SIDE RANGES

ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 14.400000 0.528571 6.900000 3 5.000000 INFINITY 0.284615 4 2.000000 1.840000 0.187342

5 0.000000 INFINITY 15.369231 6 0.000000 INFINITY 41.230770 7 0.000000 INFINITY 15.369231 8 0.00000

程序9：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 X 1000.000000 0.000000

ROW SLACK OR SURPLUS DUAL PRICES

28 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10：

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

程序11： 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); @gin(r41);@gin(r42);@gin(r43); end

Rows= 15 Vars= 15 No. integer vars= 15

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