An engine company manufactures jackets and pistons. Coating and lathe jobs are required for both jacket and piston. In order to make one jacket, 1 hour of lathe jobs and 1kg of steel are required. To manufacture a piston, 1.5-hour of lathe jobs, 1kg of steel and 0.5-hour of coating are needed. The company has weekly 750 hours of lathe jobs times, 200 hours of coating times and 600kg of steel available. The company charges $3 for a jacket and $4 for a piston respectively. Find the amount of piston and jacket to maximize profit and also write out the dual solution to primal