A company assembles printers and plotters. The printers require two hours on machine assembly and one hour of hand labor. The plotters require one hour of machine assembly and two hours of hand labor. One machine is available $12$ hours per day and $15$ hours of hand labor are available per day. If the profit on a printer is $$20$ and the profit on a plotter is $$40,$ what product mix should be manufactured per day for maximum profit. Assume there is no market problem and the all the products made can be sold.