set i /1*7/;
set j /1*4/;

parameter results(j,*);
parameter b(i), c(j), A(i,j);

b(i) = 1;
c(j) = -1;

option seed = 0;
A(i,j) = uniform(0,1);

variables obj, x(j);
equations defobj, cons(i);

defobj..
  obj =e= sum(j, c(j)*x(j));

cons(i)..
  sum(j, A(i,j)*x(j)) =l= b(i);

model lpmod /defobj, cons/;
option lp = cplex;
solve lpmod using lp min obj;
results(j,'lp') = x.l(j);

* second example uses SOCP

alias(j,k);
parameter P(i,j,k);
P(i,j,j) = 1.0e-1;

* put your formulation here

option lp=mosek;
solve socplp using lp min obj;
results(j,'socp') = x.l(j);

* third example uses A(i,.) \in [l(i),u(i)] for each row

parameters U(i,j), L(i,j);
L(i,j) = max(0,A(i,j) - 1e-1);
U(i,j) = min(1,A(i,j) + 1e-1);

* put your formulation here

option lp = cplex;
solve roblp using lp min obj;
results(j,'roblp') = x.l(j);


display results;