Solve the integer programming of this problem using branch$-$and$-$bound.

Objective: Maximize $z=3x+5y$

Subject to constraints:

$x+2y8$

$4x+y12$

$,x,y0$

$x$ and $y$ must be integers.

You may start by relaxing the integer constraint, to consider some viable real numbers, and then apply branching to enforce integer solutions.