A barge must carry steel pieces for a construction project such that the total weight of the steel pieces is under 1,500,000 kilograms (kg). Each steel piece is either a beam, which weighs 363kg, or a connector plate, which weighs 6kg. There must be at least 2 connector plates for each beam. If b is the number of beams and c is the number of connector plates, which systems of inequalities must be true?