The Council shall have power to do any public work or make any public improvement by the employment of the necessary labor and the purchase of the necessary supplies and materials with separate accounting as to each improvement so made, or to do such work by contract duly let after competitive bidding Provided, however, that the Council shall have the power to reject any and all bids. The council shall also have the power to do any public work or make any public improvement under any legally constituted plan under which the labor is furnished by any other governmental unit, department, or agency of the United States or the State of Michigan, or which is wholly or in part financed by them or either of them.