A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used $6$ workers, who together produced an average of $80$ carts per hour. Workers receive $$16$ per hour, and machine cost was $$30$ per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $$10$ per hour, while output increased by $5$ carts per hour.

a$.$ Compute labor productivity under each system. Use carts per worker per hour as the measure of labor productivity.