The treatment of models that are unbounded involves a few subtleties. Specifically, a declaration of unboundedness means that CPLEX has determined that the model has an unbounded ray. Given any feasible solution x with objective z, a multiple of the unbounded ray can be added to x to give a feasible solution with objective z-1 (or z+1 for maximization models). Thus, if a feasible solution exists, then the optimal objective is unbounded. Note that CPLEX has not necessarily concluded that a feasible solution exists. Users can call the methods IloCplex::isPrimalFeasible and IloCplex::isDualFeasible to determine whether CPLEX has also concluded that the model has a feasible solution.