Tugas RO 1 Ayzam
12
1. Decision Variable : t1, t2, t3 Objective function : max=t1+t2+t3; Constraint : 3*t1+5*t2+6*t3<=1000; 5*t1+3*t2+4*t3<=1200; t1+t2+t3<=500; Solution : Global optimal solution found. Objective value: 275.0000 Infeasibilities: 0.000000 Total solver iterations: 2 Elapsed runtime seconds: 0.01 Model Class: LP Total variables: 3 Nonlinear variables: 0 Integer variables: 0 Total constraints: 4 Nonlinear constraints: 0 Total nonzeros: 12 Nonlinear nonzeros: 0 Variable Value Reduced Cost T1 187.5000 0.000000 T2 87.50000 0.000000 T3 0.000000 0.2500000 Row Slack or Surplus Dual Price 1 275.0000 1.000000 2 0.000000 0.1250000 3 0.000000 0.1250000 4 225.0000 0.000000 2. Decision variable : A, B, C Objective function : MIN = 8*A+4*B+3*C;
-
Upload
muslich-affandi -
Category
Documents
-
view
13 -
download
3
description
aw
Transcript of Tugas RO 1 Ayzam
1. Decision Variable : t1, t2, t3Objective function : max=t1+t2+t3;Constraint :3*t1+5*t2+6*t3<=1000;5*t1+3*t2+4*t3<=1200;t1+t2+t3<=500;Solution :Global optimal solution found.Objective value: 275.0000Infeasibilities: 0.000000Total solver iterations: 2Elapsed runtime seconds: 0.01
Model Class: LP
Total variables: 3 Nonlinear variables: 0 Integer variables: 0
Total constraints: 4 Nonlinear constraints: 0
Total nonzeros: 12 Nonlinear nonzeros: 0
Variable Value Reduced Cost T1 187.5000 0.000000 T2 87.50000 0.000000 T3 0.000000 0.2500000
Row Slack or Surplus Dual Price 1 275.0000 1.000000 2 0.000000 0.1250000 3 0.000000 0.1250000 4 225.0000 0.000000
2. Decision variable : A, B, CObjective function : MIN = 8*A+4*B+3*C;
Constraint : 30*A+20*B+10*C>=120;
7*A+2*B+6*C>=42;Solution :
Global optimal solution found. Objective value: 30.00000 Infeasibilities: 0.000000 Total solver iterations: 2 Elapsed runtime seconds: 0.03
Model Class: LP
Total variables: 3 Nonlinear variables: 0 Integer variables: 0
Total constraints: 3 Nonlinear constraints: 0
Total nonzeros: 9 Nonlinear nonzeros: 0
Variable Value Reduced Cost A 0.000000 1.200000 B 3.000000 0.000000 C 6.000000 0.000000
Row Slack or Surplus Dual Price 1 30.00000 -1.000000 2 0.000000 -0.1800000 3 0.000000 -0.2000000
3. Decision varieable : x1, x2, x3, x4Objective function : max = 8*x1+6*x2-1.5*x3-3*x4;Constraint : x3+x4<=1600;x2<=1200;x1<=1000;4*x3+6*x4=9*x1+8*x2;Solution :
Global optimal solution found. Objective value: 3650.000 Infeasibilities: 0.000000 Total solver iterations: 3 Elapsed runtime seconds: 0.03
Model Class: LP
Total variables: 4 Nonlinear variables: 0 Integer variables: 0
Total constraints: 5 Nonlinear constraints: 0
Total nonzeros: 12 Nonlinear nonzeros: 0
Variable Value Reduced Cost X1 1000.000 0.000000 X2 75.00000 0.000000 X3 0.000000 0.000000 X4 1600.000 0.000000
Row Slack or Surplus Dual Price 1 3650.000 1.000000 2 0.000000 1.500000 3 1125.000 0.000000 4 0.000000 1.250000 5 0.000000 -0.7500000
4. Decision varable : m, s, pObjective function : max=(7*m+2*s+10*p)*175 - (56*m+60*s+65*s);Constraint:8*m+5*s+6.5*p<=3000;m+s+p<=120;(7*m+12*s+10*p)*90<=10000;Solution :
Global optimal solution found. Objective value: 19444.44 Infeasibilities: 0.000000 Total solver iterations: 2 Elapsed runtime seconds: 0.02
Model Class: LP
Total variables: 3 Nonlinear variables: 0 Integer variables: 0
Total constraints: 4 Nonlinear constraints: 0
Total nonzeros: 12 Nonlinear nonzeros: 0
Variable Value Reduced Cost M 0.000000 56.00000 S 0.000000 1875.000 P 11.11111 0.000000
Row Slack or Surplus Dual Price 1 19444.44 1.000000 2 2927.778 0.000000 3 108.8889 0.000000 4 0.000000 1.944444
5. Decision variable : p1, p2, p3, p4, c1, c2, c3, c4Objective function: max=4*p1+8*p2+6*p3+7*p4-5*c1-6*c2-8*c3-8*c4;Constraint : s1=2000-p1;c1+s1<=10000;s2=c1-p2+s1;c2+s2<=10000;s3=c2-p3+s2;c3+s3<=10000;s4=c3-p4+s3;c4+s4<=10000;Solution :
Global optimal solution found. Objective value: 50000.00 Infeasibilities: 0.000000 Total solver iterations: 5 Elapsed runtime seconds: 0.03
Model Class: LP
Total variables: 12 Nonlinear variables: 0 Integer variables: 0
Total constraints: 9 Nonlinear constraints: 0
Total nonzeros: 30 Nonlinear nonzeros: 0
Variable Value Reduced Cost P1 0.000000 1.000000 P2 10000.00 0.000000 P3 0.000000 0.000000 P4 10000.00 0.000000 C1 8000.000 0.000000 C2 10000.00 0.000000 C3 0.000000 2.000000
C4 0.000000 8.000000 S1 2000.000 0.000000 S2 0.000000 2.000000 S3 10000.00 0.000000 S4 0.000000 7.000000
Row Slack or Surplus Dual Price 1 50000.00 1.000000 2 0.000000 5.000000 3 0.000000 3.000000 4 0.000000 8.000000 5 0.000000 0.000000 6 0.000000 6.000000 7 0.000000 1.000000 8 0.000000 7.000000 9 10000.00 0.000000
6. Decision variable : x11, x12, x13, x14, x15, x16, x17, x21, x22, x23, x24, x25, x26, x27, x31, x32, x33, x34, x35, x36, x37, x41, x42, x43, x44, x45, x46, x47Objective function : 26*x11 + 12*x12 + 10*x13 + 18*x14 + 11*x15 + 8*x16 + 20*x17 + 28*x21 + 14*x22 + 12*x23 + 20*x24 + 13*x25 + 10*x26 + 22*x27 + 20*x31 + 26*x32+ 20*x33 + 2*x34 + 6*x35 + 22*x36 + 18*x37 + 26*x41 + 10*x42 + 4*x43 + 16*x44 + 24*x45 + 14*x46 + 21*x47;Constraint:x11 + x12 + x13 + x14 + x15 + x16 + x17 <= 660;x21 + x22 + x23 + x24 + x25 + x26 + x27 <= 301;x31 + x32 + x33 + x34 + x35 + x36 + x37 <= 271;x41 + x42 + x43 + x44 + x45 + x46 + x47 <= 99;
x11 + x21 + x31 + x41 >= 247;x12 + x22 + x32 + x42 >= 394;x13 + x23 + x33 + x43 >= 265;x14 + x24 + x34 + x44 >= 105;x15 + x25 + x35 + x45 >= 90;x16 + x26 + x36 + x46 >= 85;x17 + x27 + x37 + x47 >= 145;Solution:
Global optimal solution found. Objective value: 17592.00 Infeasibilities: 0.000000 Total solver iterations: 14 Elapsed runtime seconds: 0.03
Model Class: LP
Total variables: 28 Nonlinear variables: 0 Integer variables: 0
Total constraints: 12 Nonlinear constraints: 0
Total nonzeros: 84 Nonlinear nonzeros: 0
Variable Value Reduced Cost X11 0.000000 0.000000 X12 259.0000 0.000000 X13 166.0000 0.000000 X14 0.000000 10.00000 X15 90.00000 0.000000 X16 0.000000 0.000000 X17 145.0000 0.000000 X21 81.00000 0.000000 X22 135.0000 0.000000 X23 0.000000 0.000000 X24 0.000000 10.00000 X25 0.000000 0.000000 X26 85.00000 0.000000 X27 0.000000 0.000000 X31 166.0000 0.000000 X32 0.000000 20.00000 X33 0.000000 16.00000 X34 105.0000 0.000000 X35 0.000000 1.000000 X36 0.000000 20.00000 X37 0.000000 4.000000 X41 0.000000 6.000000
X42 0.000000 4.000000 X43 99.00000 0.000000 X44 0.000000 14.00000 X45 0.000000 19.00000 X46 0.000000 12.00000 X47 0.000000 7.000000
Row Slack or Surplus Dual Price 1 17592.00 -1.000000 2 0.000000 2.000000 3 0.000000 0.000000 4 0.000000 8.000000 5 0.000000 8.000000 6 0.000000 -28.00000 7 0.000000 -14.00000 8 0.000000 -12.00000 9 0.000000 -10.00000 10 0.000000 -13.00000 11 0.000000 -10.00000 12 0.000000 -22.00000
7. Decision variable : x11, x12, x13, x21, x22Objective function : min= x11*70 + x12*200 + x13*620 + x21*1.55 + x22*1.3;Constraint:(x11*100 + x12*240 + x13*400)*0.09 + (x21*0.1 + x22*0.08)>=2350;x11 + x12 + x13<=1500;100*x11 + 240*x12 + 400*x13 + x21 + x22<=26500;x11 <= 50;x12 <= 25;x13 <= 10;x21 <= 5000;Solution :
Global optimal solution found. Objective value: 30400.00 Infeasibilities: 0.000000 Total solver iterations: 0 Elapsed runtime seconds: 0.09
Model Class: LP
Total variables: 5 Nonlinear variables: 0 Integer variables: 0
Total constraints: 8 Nonlinear constraints: 0
Total nonzeros: 22 Nonlinear nonzeros: 0
Variable Value Reduced Cost X11 50.00000 0.000000 X12 25.00000 0.000000 X13 5.000000 0.000000 X21 5000.000 0.000000 X22 8500.000 0.000000
Row Slack or Surplus Dual Price 1 30400.00 -1.000000 2 0.000000 -25.00000 3 1420.000 0.000000 4 0.000000 0.7000000 5 0.000000 85.00000 6 0.000000 172.0000 7 5.000000 0.000000 8 0.000000 0.2500000
8. Decision variable :x11, x14, x17, x22, x25, x28, x33, x36, x39, x310Objective function : min=0.05*x11 + 0.07*x14 + 0.13*x17 + 0.05*x22 + 0.07*x25 + 0.13*x28 + 0.05*x33 + 0.07*x36 + 0.13*x39 + 0.13*x310 ;Constraint:x11 + x14 + x17 <= 3000;x22 + x25 + x28 <= 2500;x33 + x36 + x39 + x310 <= 7000;x11 + x22 + x33 + x14 + x25 + x36 + x17 + x28 + x39 + x310 >= 10000;x11 <= 1100;x22 <= 1100;x33 <= 1100;x14 <= 1500;x25 <= 1500;x36 <= 1500;x17 <= 2500;
x28 <= 2500;x39 <= 2500;X310 <= 2500;Solution :
Global optimal solution found. Objective value: 772.0000 Infeasibilities: 0.000000 Total solver iterations: 4 Elapsed runtime seconds: 0.39
Model Class: LP
Total variables: 10 Nonlinear variables: 0 Integer variables: 0
Total constraints: 15 Nonlinear constraints: 0
Total nonzeros: 40 Nonlinear nonzeros: 0
Variable Value Reduced Cost X11 1100.000 0.000000 X14 1500.000 0.000000 X17 400.0000 0.000000 X22 1100.000 0.000000 X25 1400.000 0.000000 X28 0.000000 0.6000000E-01 X33 1100.000 0.000000 X36 1500.000 0.000000 X39 0.000000 0.000000 X310 1900.000 0.000000
Row Slack or Surplus Dual Price 1 772.0000 -1.000000 2 0.000000 0.000000 3 0.000000 0.6000000E-01 4 2500.000 0.000000 5 0.000000 -0.1300000 6 0.000000 0.8000000E-01
7 0.000000 0.2000000E-01 8 0.000000 0.8000000E-01 9 0.000000 0.6000000E-01 10 100.0000 0.000000 11 0.000000 0.6000000E-01 12 2100.000 0.000000 13 2500.000 0.000000 14 2500.000 0.000000 15 600.0000 0.000000
