Maximize $w=2x+3y+6z$ subject to
$2x+y+z \le 5$
$3y+2z \le 6$
$x,y,z \ge 0$
Is the optimal solution unique? Justify your answer.
I tried to solve it by Simplex method. In the second iteration, I got the optimal solution condition and the optimum solution is $z=3,\; x=1, y=0$. . Correct me if I have done anything wrong.
Also how to justify that there exists or doesn't an alternate optimum?