!Illustrating how, when there are alternative optima,
   Simplex method chooses an extreme point solution, whereas
   Interior Point/Barrier (without crossover) chooses
      an interior solution that, loosely speaking, is an average
      of all extreme point solutions.
   When there are alternative optima, and there are secondary
   multi-critera, some users may prefer the unique solution of
   the barrier method to the essentially random arbitrary choice
   of one of the extreme point optima.
 Keywords: Alternative optima, Barrier method, Crossover, Interior point method
           Multi-criteria, Simplex method;

SUBMODEL astro:
! This model has 3 alternative extreme point optima;
 MAX= 15*a + 30*c + 45*m;
         a  + 2*c  + 3*m <= 120;
         a           + m <=  60;
                c    + m <=  50;
ENDSUBMODEL

CALC:
  @SET( 'TERSEO',0);   ! Output level (0:verb, 1:terse, 2:only errors, 3:none);
! Do some cleanup rounding of output;
  @SET( 'PRECIS', 6); ! Precision (in digits) for standard reports;
  @SET( 'CUTOFF', 0.1E-6); ! Cutoff(Show as zero) solution values smaller than this;

  @WRITE(' Solve with Primal Simplex:', @NEWLINE( 1));
  @SET( 'SOLVEL', 1);  ! Linear solver (0:LINGO decides,1:primal,2:dual,3:barrier);
  @SOLVE( astro);

  @WRITE(' Solve with Dual Simplex:', @NEWLINE( 1));
  @SET( 'SOLVEL', 2);  ! Linear solver (0:LINGO decides,1:primal,2:dual,3:barrier);
  @SOLVE( astro);

  @WRITE(' Solve with Barrier without crossover:', @NEWLINE( 1));
  @SET( 'SOLVEL', 3); ! Linear solver (0:LINGO decides,1:primal,2:dual,3:barrier);
  @SET( 'BCROSS', 0); ! Crossover to vertex solution with barrier solver(0:n, 1:y);
  @SOLVE( astro);
ENDCALC