Example 1: Linear Programming

The linear programming problem in the standard form

{\rm {min}} \,\, f(x) = -x_1 - 3x_2

subject to:

x_1 + x_2 + x_3 = 1.5
x_1 + x_2 - x_4 = 0.5
x_1 + x_5 = 1.0
x_2 + x_6 = 1.0
x_i \ge 0, \,\,\,\, {\rm {for}} \,\,\, i = 1, \ldots , 6

is solved.

import com.imsl.math.*;

public class LinearProgrammingEx1 {
    public static void main(String args[]) throws Exception {
        double[][] a = {
            {1.0, 1.0, 1.0, 0.0, 0.0, 0.0},
            {1.0, 1.0, 0.0, -1.0, 0.0, 0.0},
            {1.0, 0.0, 0.0, 0.0, 1.0, 0.0},
            {0.0, 1.0, 0.0, 0.0, 0.0, 1.0}
        };
        double[] b = {1.5, 0.5, 1.0, 1.0};
        double[] c = {-1.0, -3.0, 0.0, 0.0, 0.0, 0.0};
        
        LinearProgramming zf = new LinearProgramming(a, b, c);
        
        zf.solve();
        new PrintMatrix("Solution").print(zf.getPrimalSolution());
    }
}

Output

Solution
    0   
0  0.5  
1  1    
2  0    
3  1    
4  0.5  
5  0
Link to Java source.