#
# A Basic LP Example for GLPK
#
# We will make 5 variables, and 3 constraints (one of each type)
#
# min x_1 + x_2 -3x_3 
# st. x_1 - x_2        + x_4       = 3
#     x_1        +3x_3       + x_5 >= 10
#           x_2  - x_3             <= 4
#     x_1,  x_2,   x_3,  x_4,  x_5 >= 0

set I; 
/* variable labels */

set JG;
set JE;
set JL;
/* constraint labels, for Greater-than, Equal-to, and Less-than constraints. */

param c{i in I};
/* cost of variables */

param bG{j in JG};
param bE{j in JE};
param bL{j in JL};
/* right-hand-side of constraints */

param AG{j in JG, i in I};
param AE{j in JE, i in I};
param AL{j in JL, i in I};
/* values of the matrix A */

var x{i in I} >= 0;
/* a non-negative variable vector */

minimize cost: sum{i in I} c[i] * x[i];
/* the optimization function */

s.t. boundG{j in JG}: sum{i in I} AG[j,i] * x[i] <= bG[j];
s.t. boundE{j in JE}: sum{i in I} AE[j,i] * x[i] == bE[j];
s.t. boundL{j in JL}: sum{i in I} AL[j,i] * x[i] >= bL[j];
/* the constraints */

/* mark the beginning of the data */
data;

set I := x1 x2 x3 x4 x5;
set JG := c2;
set JE := c1;
set JL := c3;

param c := x1  1
           x2  1
           x3 -3
           x4  0
           x5  0;

param bG := c2 10;
param bE := c1  3;
param bL := c3  4;

param AG:  x1  x2  x3  x4  x5 :=
        c2 1.0 0.0 3.0 0.0 1.0;

param AE:  x1  x2  x3  x4  x5 :=
        c1  1  -1   0   1   0;
 
param AL:  x1  x2  x3  x4  x5 :=
        c3  0   1  -1   0   0;


end;