Two products, A and B $,$ are made using two operations, operation $1$ and operation $2.$ Each unit of A requires $2$ hours on operation $1$ and $4$ hours on operation $2.$ Each unit of B requires $4$ hours on operation $1$ and $4$ hours on operation $2.$ The available time for operation $1$ is $16$ hours. The available time for operation $2$ is $24$ hours. Product A sells for $$4$ profit per unit whereas product B sells for $$5$ profit per unit. How many units of A and B should be produced to make the largest profit? Please formulate an LP model and solve the LP model graphically.