[SerializableAttribute]
public class SimplexLPSolver : ICloneable

<SerializableAttribute> _
Public Class SimplexLPSolver _
	Implements ICloneable

[SerializableAttribute]
public ref class SimplexLPSolver : ICloneable

A linear programming (LP) problem optimizes a linear objective function subject to a set of linear constraints, and optionally subject to a set of variable bounds. The simplex method solves LP problems by constructing a solution at a vertex of a simplex, then walking along edges of the simplex to vertices with successively higher values of the objective function until the optimum is reached. For example:

CopyC#

Maximize
Z = X1 + 4 X2 + 9 X3

Subject To
X1 + X2 <= 5
X1 + X3 >= 10
- X2 + X3 = 7

Bounds
0 <= X1 <= 4
0 <= X2 <= 1

The Solve() method on SimplexLPSolver accepts a vector of coefficients representing the objective function, a matrix of constraint coefficients, a vector of right-hand sides, the number of each constraint type (less than, greater than, or equal to), and optionally vectors of lower and upper variable bounds. Thus:

CopyC#

DoubleVector obj = new DoubleVector( "[1 4 9]" );
DoubleMatrix constraints = new DoubleMatrix( "3x3 [1 1 0  1 0 1  0 -1 1]" );
DoubleVector rhs = new DoubleVector( "[5 10 7]" );
int numLessThan = 1;
int numGreaterThan = 1;
int numEqual = 1;
DoubleVector upperBounds = new DoubleVector( "[4 1 Infinity]" );

SimplexLPSolver solver = new SimplexLPSolver();
DoubleVector solution = solver.Solve( obj, constraints, rhs, numLessThan, numGreaterThan,
                                      numEqual, upperBounds );

It is important to check the Status property after optimization, which returns a value from the SimplexLPSolver.SolutionStatus enum, since your problem may be unbounded or infeasible.

System..::.Object
  CenterSpace.NMath.Analysis..::.SimplexLPSolver