Maximize z= 2x1+3x2+x3 
subject to 
1x1-x2+2x3 <=3, 
3x1+x2+2x3 <=3, 
6x1+7x2+2x3 <=8;

Tableau #3
x1     x2     x3     s1     s2     s3     z             
-1     0      0      1      -4/3   1/3    0      5/3    
5/4    0      1      0      7/12   -1/12  0      13/12  
1/2    1      0      0      -1/6   1/6    0      5/6    
3/4    0      0      0      1/12   5/12   1      43/12  


Optimal Solution: z = 43/12; x1 = 0, x2 = 5/6, x3 = 13/12, s1= 29/7, s2 = 0, s3 = 0 


DUAL
Minimize z= 3w1+3w2+8w3 
subject to 
1w11+3w2+6w3 >=2, 
-1w1+1w2+7w3 >=3, 
2w11+2w2+2w3 >=1;

Optimal Solution: z = 43/12; w1 = 0, w2 = 1/12, w3 = 5/12 , s1 =11/16, s2 = 0, s3 = 0

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Maximize z= 2x1+x2+3x3 
subject to 
2x1+1x2+1x3 <=14, 
0x1+1x2-2x3 >=3, 
1x1+2x2-3x3 =12;


Tableau #4
x1     x2     x3     s1     s2     s3     s4     z             
3/5    0      1      2/5    0      0      1/5    0      16/5   
7/5    1      0      3/5    0      0      -1/5   0      54/5   
0      0      0      0      0      1      1      0      0      
1/5    0      0      -1/5   1      0      -3/5   0      7/5    
6/5    0      0      9/5    0      0      2/5    1      102/5     

Optimal Solution: z = 102/5; x1 = 0, x2 = 54/5, x3 = 16/5, s1 = 0, s2 = 7/5, a1 = 0, a2 =0;



DUAL

Minimize z= 14w1-3w2+12w3-12w4
subject to 
2w1+0w2+1w3-1w4 >=2, 
1w1-1w2+2w3-2w4 >= 1, 
1w1+2w2-3w3 +3w4>=3;



Tableau #4
w1     w2     w3     w4     s1     s2     s3     -z            
0      -1/5   0      0      1      -7/5   -3/5   0      6/5    
1      1/5    0      0      0      -3/5   -2/5   0      9/5    
0      3/5    -1     1      0      1/5    -1/5   0      2/5    
0      7/5    0      0      0      54/5   16/5   1      -102/5 

Optimal Solution: z = 102/5; w1 = 9/5, w2 = 0, w3 = 0, w4 = 2/5, s1 = 6/5, s2 =0, s3 =0