Problem $2.(25$ points$).$ Solve the following $LP$ using Python and Gurobi. Report the Python code you used, the optimal solution and the optimal value, $orif$ the problem $is$ unbounded $or$ infeasible.

max $z=4x_1+6x_2+3x_3+5x_4+7x_5+2x_6+8x_7+9x_8+4x_9$

Subject $to$:

$x_1+x_2+x_{3}8$

$x_4+x_5+x_{6}16$

$x_7+x_8+x_9=25$

$x_1+x_4+x_{7}10$

$x_2+x_5+x_{8}12$

$x_3+x_6+x_9=15$

$x_1+x_5+x_{9}18$

$x_3+x_5+x_{7}20$

$x_2+x_4+x_{6}14$

$x_1,x_2,....x_{9}0.$