SOLUCION DE LOS PROBLEMAS FORMULADOS DEL LIBRO DE TAHA EN LINGO

P2 de taha(pag)

Max=10*(x11+x12)+12*(x21+x22);

x11+x21<=35*y1;

x12+x22<=35*y2;

y1+y2=1;

x11<=20*y1;

x21<=10*y1;

x12<=12*y2;

x22<=22*y2;

@gin(x11);

@gin(x12);

@gin(x21);

@gin(x22);

@bin(y1);

@bin(y2);

Solución:

Objective value:                 384.0000

 Branch count:                           0

                       Variable           Value        Reduced Cost

                            X11       0.0000000E+00       0.0000000E+00

                            X12        12.00000           0.0000000E+00

                            X21       0.0000000E+00       0.0000000E+00

                            X22        22.00000           0.0000000E+00

                             Y1       0.0000000E+00       0.0000000E+00

                             Y2        1.000000           -64.00000

                            Row    Slack or Surplus      Dual Price

                              1        384.0000            1.000000

                              2       0.0000000E+00       0.0000000E+00

                              3        1.000000           0.0000000E+00

                              4       0.0000000E+00        320.0000

                              5       0.0000000E+00        10.00000

                              6       0.0000000E+00        12.00000

                              7       0.0000000E+00        10.00000

                              8       0.0000000E+00        12.00000

Elegimos la segunda opción de producción generando una utilidad de S/. 384.

P3 del libro taha (pag)

Max=25*x11+30*x21+22*x31+25*x12+30*x22+22*x32;

3*x11+4*x21+5*x31<=100*y1;

4*x11+3*x21+6*x31<=100*y1;

3*x12+4*x22+5*x32<=90*y2;

4*x12+3*x22+6*x32<=120*y2;

y1+y2=1;

@gin(x11);

@gin(x21);

@gin(x31);

@gin(x12);

@gin(x22);

@gin(x32);

@bin(y1);

@bin(y2);

Solucion:

Objective value:                 780.0000     

 Branch count:                           5

                       Variable           Value        Reduced Cost

                            X11        12.00000           0.0000000E+00

                               Se realiza 12unid. Del producto 1

                            X21        16.00000            3.333332

                               Se realiza 16unid. Del producto 2

                            X31       0.0000000E+00        19.66667

                            X12       0.0000000E+00       0.0000000E+00

                            X22       0.0000000E+00       0.0000000E+00

                            X32       0.0000000E+00        18.71428

                             Y1        1.000000           0.0000000E+00

                             Y2       0.0000000E+00        83.33333

                            Row    Slack or Surplus      Dual Price

                              1        780.0000            1.000000

                              2       0.0000000E+00        8.333333

                              3        4.000000           0.0000000E+00

                              4       0.0000000E+00        6.428571

                              5       0.0000000E+00        1.428571

                              6       0.0000000E+00        833.3333

Elegimos la primera opción de producción generando una utilidad de S/.780.

P5 del libro de taha(pag)

Max=25*x1+30*x2+45*x3;

3*x1+4*x2+5*x3<=100;

4*x1+3*x2+6*x3<=100;

x3>=5;

@gin(x1);

@gin(x2);

@gin(x3);

Solución:

Objective value:                 825.0000

 Branch count:                           1

                       Variable           Value        Reduced Cost

                             X1       0.0000000E+00        5.000000

                             X2        11.00000           0.0000000E+00

                             X3        11.00000            15.00000

                            Row    Slack or Surplus      Dual Price

                              1        825.0000            1.000000

                              2        1.000000           0.0000000E+00

                              3        1.000000           0.0000000E+00

                              4        6.000000           0.0000000E+00

Se tiene que realizar 11 unidades del producto 2 y 11unidades del producto 3 para obtener  el beneficio óptimo de S/. 825.