//
//    Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
//    File:    midual1.cs
//
//    Purpose:  Demonstrates how to compute dual values with
//              respect to a fixed integer solution for a MIO problem.
//
//              minimize    500 s1 + 300 s2 + 10 x1 + 14 x2
//              subject to  x1 + x2 >= 100
//                          0 <= x1 <= 70 s1
//                          0 <= x2 <= 80 s2
//                          s1, s2 - binary
//
using System;
using mosek.fusion;

namespace mosek.fusion.example
{
  public class mico1
  {
    public static void Main(string[] args)
    {
      /* M is the initial mixed-integer model */
      using (Model M = new Model("midual1"))
      {
        Variable x = M.Variable("x", 2, Domain.GreaterThan(0));
        Variable s = M.Variable("s", 2, Domain.Binary());

        M.Objective(ObjectiveSense.Minimize,
                    Expr.Add(Expr.Dot(new double[]{10,14}, x), 
                             Expr.Dot(new double[]{500,300}, s)));

        M.Constraint("demand",
                     Expr.Sum(x), Domain.GreaterThan(100));
        M.Constraint("production",
                     Expr.Sub(x, Expr.MulElm(new double[]{70,80}, s)), 
                     Domain.LessThan(0));

        M.Solve();

        if (M.GetProblemStatus() != ProblemStatus.PrimalFeasible)
          throw new System.Exception("Unsuitable problem status, exiting");

        Console.WriteLine("x = {0}, {1}", x.Level()[0], x.Level()[1]);

        /* F is the continuous fixed model */
        using (Model F = M.GetFixedModel())
        {
          F.Solve();

          if (F.GetProblemStatus() != ProblemStatus.PrimalAndDualFeasible)
            throw new System.Exception("Unsuitable problem status, exiting");

          Constraint demand = F.GetConstraint("demand");
          Constraint production = F.GetConstraint("production");
          Variable xfix = F.GetVariable("x");

          Console.WriteLine("xfix = {0}, {1}", xfix.Level()[0], xfix.Level()[1]);
          Console.WriteLine("demand dual = {0}", demand.Dual()[0]);
          Console.WriteLine("production dual = {0}, {1}", production.Dual()[0], production.Dual()[1]);
        }
      }
    }
  }
}