int nbsets = ...;
int nbelements = ...;
range elements 1..nbelements;
range sets 1..nbsets;
int cost[sets] = ...;
int covers[elements,sets]= ...;
var int x[sets] in 0..1;

minimize 
   sum (j in sets) cost[j]*x[j]
subject to
  forall(i in elements)
     sum(j in sets) covers[i,j]*x[j]>= 1;