# C# Linear Programming Example

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```using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.Examples.CSharp
{
class LinearProgrammingExample
{
/// <summary>
/// A .NET example in C# showing how to solve a linear system using linear programming and
/// the primal simplex method.
/// </summary>
static void Main( string[] args )
{
// A farmer has 640 acres of farmland. It can be planted with wheat, barley, corn or a
// combination of the three. The farmer wishes to maximize his profit subject to the
// limits on land, fertilizer, and water.

// Currently, wheat is \$3.38/bushel. The farmer can expect a yield of 55 bushels/acre.
double wheatPrice = 3.38;
double wheatYield = 55.0;
double wheatRevenuePerAcre = wheatPrice * wheatYield;

// Currently, barley is \$1.98/bushel. The farmer can expect a yield of 75 bushels/acre.
double barleyPrice = 1.98;
double barleyYield = 75.0;
double barleyRevenuePerAcre = barleyPrice * barleyYield;

// Currently, corn is \$1.70/bushel. The farmer can expect a yield of 110 bushels/acre.
double cornPrice = 1.70;
double cornYield = 110.0;
double cornRevenuePerAcre = cornPrice * cornYield;

Console.WriteLine();

// Therefore, the objective function is:
Console.Write( "Maximize " + wheatRevenuePerAcre + "w + " );
Console.WriteLine( barleyRevenuePerAcre + "b + " + cornRevenuePerAcre + "c" );
Console.WriteLine( "where" );
Console.WriteLine();

var revenue = new DoubleVector( wheatRevenuePerAcre, barleyRevenuePerAcre, cornRevenuePerAcre );
var lpProblem = new LinearProgrammingProblem( revenue );

// The farmer has 8,000 lbs of nitrogen fertilizer. Its known that wheat requires
// 12 lb/acre, barley 5 lb/acre and corn 22 lb/acre.
Console.WriteLine( "12w + 5b + 22c <= 8000" );
lpProblem.AddUpperBoundConstraint( new DoubleVector( 12.0, 5.0, 22.0 ), 8000.0 );

// The farmer has 22,000 lbs of phosphate fertilizer. Its known that wheat requires
// 30 lb/acre, barley 8 lb/acre and corn 50 lb/acre.
Console.WriteLine( "30w + 8b + 50c <= 22000" );
lpProblem.AddUpperBoundConstraint( new DoubleVector( 30.0, 8.0, 50.0 ), 22000.0 );

// The farmer has a permit for 1,000 acre-feet of water. Wheat requires 1.5 ft of water,
// barley requires 0.7 and corn 2.2.
Console.WriteLine( "1.5w + 0.7b + 2.2c <= 1200" );
lpProblem.AddUpperBoundConstraint( new DoubleVector( 1.5, 0.7, 2.2 ), 1200.0 );

// The farmer has a maximum of 640 acres for planting.
Console.WriteLine( "w + b + c <= 640" );
lpProblem.AddUpperBoundConstraint( new DoubleVector( 1.0, 1.0, 1.0 ), 640.0 );
for ( int i = 0; i < revenue.Length; i++ )
{
}
// Create an LP solver
var solver = new PrimalSimplexSolver();

// Solve
solver.Solve( lpProblem );

// Was a finite solution found?
Console.WriteLine();
if ( solver.Result == PrimalSimplexSolver.SolveResult.Optimal )
{
Console.WriteLine( "solution: " + solver.OptimalX.ToString( "f0" ) );
Console.WriteLine();
Console.WriteLine( "optimal value: " + solver.OptimalObjectiveFunctionValue.ToString( "f0" ) );
}
Console.WriteLine();

// Lets say the farmer is also contractually obligated to farm at least 10 acres
// of barley.
Console.WriteLine( "Add variable bound: b >= 10" );

// Solve again
solver.Solve( lpProblem );

// Good?
Console.WriteLine();
if ( solver.Result == PrimalSimplexSolver.SolveResult.Optimal )
{
Console.WriteLine( "solution: " + solver.OptimalX.ToString( "f0" ) );
Console.WriteLine();
Console.WriteLine( "optimal value: " + solver.OptimalObjectiveFunctionValue.ToString( "f0" ) );
}

Console.WriteLine();
Console.WriteLine( "Press Enter Key" );