Model version 0
************************************************************************


! Lingo model Ex3;
! Peter Lohmander 171110;

model:

! Initial conditions;
V0 = 300;
PA0 = 20;

! Other parameters;
PA1 = 20;
c = 50;
PB1 = 0;
PB2 = 0;
r = 0.03;
r2 = 0.03;
a = 0.05;
K = 400;

Prof1 = PA0*(V0 - V1)- c;

Prof2 = (PA1*(V2 - V1)-c)/(@exp(r*t)-1);

Prof3 = PB1*V0*1/r2;

Prof4 = (V2-V1)/t*(PB2*1/r2+PB1*1/(r2*r2));

Prof = Prof1 + Prof2 + Prof3 + Prof4;

@free(Prof1);
@free(Prof2);
@free(Prof3);
@free(Prof4);
@free(Prof);



t>5;
t<50;
V1>20;
V1 < V0;

V2 = 1/(1/K+(1/V1-1/K)*@exp(-a*t));

max = Prof;

end

***********************************************************************************

Results from version 0
**********************

  Local optimal solution found.
  Objective value:                              6397.031
  Infeasibilities:                              0.000000
  Total solver iterations:                            38
  Elapsed runtime seconds:                          0.04

  Model Class:                                       NLP

  Total variables:                      7
  Nonlinear variables:                  3
  Integer variables:                    0

  Total constraints:                   10
  Nonlinear constraints:                2

  Total nonzeros:                      19
  Nonlinear nonzeros:                   5



                                Variable           Value        Reduced Cost
                                      V0        300.0000            0.000000
                                     PA0        20.00000            0.000000
                                     PA1        20.00000            0.000000
                                       C        50.00000            0.000000
                                     PB1        0.000000            0.000000
                                     PB2        0.000000            0.000000
                                       R       0.3000000E-01        0.000000
                                      R2       0.3000000E-01        0.000000
                                       A       0.5000000E-01        0.000000
                                       K        400.0000            0.000000
                                   PROF1        4993.625            0.000000
                                      V1        47.81876            0.000000
                                   PROF2        1403.406            0.000000
                                      V2        120.4430            0.000000
                                       T        23.09396            0.000000
                                   PROF3        0.000000            0.000000
                                   PROF4        0.000000            0.000000
                                    PROF        6397.031            0.000000

**************************************************************************************


              PROF*    V1*      t*     V2*

M0            6397     47.8   23.1   120.4

M1
(r=r2=0.02)   7577     82.8   19.2   162.2

M2           13598     97.7   17.7   175.9
(PB1=0.5)

M3           36480    144.4   11.6   201.0
(PB1=2)

M4            7645     82.6   19.6   163.7
(PB2=10)   

**************************************************************************************