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?
/* Objective function */ max: 2x + 3y + 6z; 2x+y+z <= 5; 3y+2z <= 6;
/* Variable bounds */ x >= 0; y >= 0; z >= 0;
x = 1, y = 0, z = 3
Optimal solution 20 after 2 iter. Relative numeric accuracy ||*|| = 0
MEMO: lp_solve version 5.5.2.5 for 32 bit OS, with 64 bit REAL variables. In the total iteration count 2, 0 (0.0%) were bound flips. There were 0 refactorizations, 0 triggered by time and 0 by density. ... on average 2.0 major pivots per refactorization. The largest [LUSOL v2.2.1.0] fact(B) had 3 NZ entries, 1.0x largest basis. The constraint matrix inf-norm is 3, with a dynamic range of 3. Time to load data was 0.003 seconds, presolve used 0.008 seconds, ... 0.006 seconds in simplex solver, in total 0.017 seconds.