Fancy Toy Factory wants to determine their production mix, with the goal of maximizing profits. The factory produces toy cars and toy trucks. The profit on each car is $$3$ while the profit on each truck is $$5.$ The toys are manufactured with a machine called a plastic extruder which utilizes plastic resins. Each car requires $1$ lbs$.$ of plastic resins to produce while each truck require $2$ lbs$.$ The daily supply of plastic resins is limited to at most $1800$ pounds. Each car requires $2$ hours of machine time, and each truck also requires $2$ hours. At the moment the factory has a total of $2500$ hours available. In addition, at most a total of $2000$ toys can be sold.