線性規劃具體實例

1、例子

2、MATLAB求解

2.1 代碼

c=[2;3;1];
a=[1 4 2;3 2 0];
b=[8;6];
[x,y]=linprog(c,-a,-b,[],[],zeros(3,1))

2.2 結果

Optimization terminated.

x =

    0.8066
    1.7900
    0.0166
y =

    7.0000

3、lingo求解

3.1 代碼

min=2*x1+3*x2+x3;
x1+4*x2+2*x3>=8;
3*x1+2*x2>=6;
x1>=0;
x2>=0;
x3>=0;

3.2 結果

 Global optimal solution found.
  Objective value:                              7.000000
  Infeasibilities:                              0.000000
  Total solver iterations:                             3

  Model Class:                                        LP

  Total variables:                      3
  Nonlinear variables:                  0
  Integer variables:                    0

  Total constraints:                    6
  Nonlinear constraints:                0

  Total nonzeros:                      11
  Nonlinear nonzeros:                   0

                                Variable           Value        Reduced Cost
                                      X1       0.8000000            0.000000
                                      X2        1.800000            0.000000
                                      X3        0.000000            0.000000

                                     Row    Slack or Surplus      Dual Price
                                       1        7.000000           -1.000000
                                       2        0.000000          -0.5000000
                                       3        0.000000          -0.5000000
                                       4       0.8000000            0.000000
                                       5        1.800000            0.000000
                                       6        0.000000            0.000000

4、對比

         從MATLAB和LINGO可以看出，結果是一致的，說明可以選擇其中一種方式進行求解；