Solve the following problem by the two phase simplex method

Solve the following problem by the two phase simplex method. Kindly show each step:

Maximize x₁ + 3x₂ -x₃

subject to 2x₁ + x₂ +3x_{3 >=3}

-x₁ + x_{2   >= 1}

-x₁ - 5x₂ + x_{3 <=4}

x_1, x₂, x_{3 >= 0}

Solution

Maximize x1 + 3x2 -x3

subject to 2x1 + x2 +3x3 >=3

-x1 + x2 >= 1

-x1 - 5x2 + x3 <=4

x1, x2, x3 >= 0

Tableau #1
x1 x2 x3 s1 s2 s3 s4 s5 s6 p   
2 1 3 -1 0 0 0 0 0 0 3
-1 1 0 0 -1 0 0 0 0 0 1
-1 -5 1 0 0 1 0 0 0 0 4
1 0 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 -1 0 0
-1 -3 1 0 0 0 0 0 0 1 0

Tableau #2
x1 x2 x3 s1 s2 s3 s4 s5 s6 p   
2 1 0 -1 0 0 0 0 3 0 3
-1 1 0 0 -1 0 0 0 0 0 1
-1 -5 0 0 0 1 0 0 1 0 4
1 0 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 -1 0 0
-1 -3 0 0 0 0 0 0 1 1 0

Tableau #3
x1 x2 x3 s1 s2 s3 s4 s5 s6 p   
0.666667 0.333333 0 -0.333333 0 0 0 0 1 0 1   
-1 1 0 0 -1 0 0 0 0 0 1   
-1.66667 -5.33333 0 0.333333 0 1 0 0 0 0 3   
1 0 0 0 0 0 -1 0 0 0 0   
0 1 0 0 0 0 0 -1 0 0 0   
0.666667 0.333333 1 -0.333333 0 0 0 0 0 0 1   
-1.66667 -3.33333 0 0.333333 0 0 0 0 0 1 -1

Tableau #4
x y z s1 s2 s3 s4 s5 s6 p   
0.666667 0 0 -0.333333 0 0 0 0.333333 1 0 1   
-1 0 0 0 -1 0 0 1 0 0 1   
-1.66667 0 0 0.333333 0 1 0 -5.33333 0 0 3   
1 0 0 0 0 0 -1 0 0 0 0   
0 1 0 0 0 0 0 -1 0 0 0   
0.666667 0 1 -0.333333 0 0 0 0.333333 0 0 1   
-1.66667 0 0 0.333333 0 0 0 -3.33333 0 1 -1

Tableau #5
x y z s1 s2 s3 s4 s5 s6 p   
1 0 0 -0.333333 0.333333 0 0 0 1 0 0.666667
-1 0 0 0 -1 0 0 1 0 0 1   
-7 0 0 0.333333 -5.33333 1 0 0 0 0 8.33333   
1 0 0 0 0 0 -1 0 0 0 0   
-1 1 0 0 -1 0 0 0 0 0 1   
1 0 1 -0.333333 0.333333 0 0 0 0 0 0.666667
-5 0 0 0.333333 -3.33333 0 0 0 0 1 2.33333   

Tableau #6
x1 x2 x3 s1 s2 s3 s4 s5 s6 p   
1 0 0 -0.333333 0.333333 0 0 0 1 0 0.666667
-1 0 0 0 -1 0 0 1 0 0 1   
-7 0 0 0.333333 -5.33333 1 0 0 0 0 8.33333   
-1 0 0 0 0 0 1 0 0 0 0   
-1 1 0 0 -1 0 0 0 0 0 1   
1 0 1 -0.333333 0.333333 0 0 0 0 0 0.666667
-5 0 0 0.333333 -3.33333 0 0 0 0 1 2.33333   

Tableau #7
x1 x2 x3 s1 s2 s3 s4 s5 s6 p   
1 0 0 -0.333333 0.333333 0 0 0 1 0 0.666667
0 0 0 -0.333333 -0.666667 0 0 1 1 0 1.66667   
0 0 0 -2 -3 1 0 0 7 0 13
0 0 0 -0.333333 0.333333 0 1 0 1 0 0.666667
0 1 0 -0.333333 -0.666667 0 0 0 1 0 1.66667   
0 0 1 0 0 0 0 0 -1 0 0   
0 0 0 -1.33333 -1.66667 0 0 0 5 1 5.66667   

Tableau #8
x1 x2 x3 s1 s2 s3 s4 s5 s6 p   
1 0 0 0 0 0 -1 0 0 0 0
0 0 0 -1 0 0 2 1 3 0 3
0 0 0 -5 0 1 9 0 16 0 19   
0 0 0 -1 1 0 3 0 3 0 2
0 1 0 -1 0 0 2 0 3 0 3
0 0 1 0 0 0 0 0 -1 0 0
0 0 0 -3 0 0 5 0 10 1 9

No optimal solution exists for this problem.