# Maximising a Linear Programming Problem

Maximize $w=2x+3y+6z$ subject to

$2x+y+z \le 5$

$3y+2z \le 6$

$x,y,z \ge 0$

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?

• i have got $$30,x=0,y=0,z=5$$ – Dr. Sonnhard Graubner Sep 18 '17 at 12:55
• That's right, $(0,0,5)$ is the optimal and unique. – A.Γ. Sep 18 '17 at 13:04
• Can you please provide the solution? Also how to justify that the optimal solution is unique? – Balaji Sep 18 '17 at 13:08
• There was some mistake in the second constraint. I have corrected it. Please check it. – Balaji Sep 18 '17 at 13:17
• @Balaji OK, the corrected problem has indeed the solution after two iterations as $(1,0,3)$. No non-basic column has zero in the top row of the simplex tableau, therefore, the solution is unique. – A.Γ. Sep 18 '17 at 13:30