Consider the following problem:

Maximize $z=3x_1+4x_2+2x_3$

subject $to$:

$2x_1+3x_2+2x_{3}7$

$x_1+x_2+x_{3}4$

$x_1,x_2,x_{3}in{Z}^{+}$

Use dynamic programming to solve the problem.