Solve the linear programming problem using the simplex metho

Solve the linear programming problem using the simplex method. Maximize p=2x_1 +3x_2 +4x_3 subject to x_1 + x_3

Solution

The maximum value of P = 102 when x₁ = 24, x₂ = 18, x₃ = 0

Tableau #1
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 0 1 1 0 0 0 0 0 24   
0 1 1 0 1 0 0 0 0 18   
1 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-2 -3 -4 0 0 0 0 0 1 0

Tableau #2
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 0 1 1 0 0 0 0 0 24   
0 1 1 0 1 0 0 0 0 18   
-1 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-2 -3 -4 0 0 0 0 0 1 0

Tableau #3
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 0 1 1 0 0 0 0 0 24   
0 1 1 0 1 0 0 0 0 18   
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-2 -3 -4 0 0 0 0 0 1 0

Tableau #4
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 0 1 1 0 0 0 0 0 24   
0 1 1 0 1 0 0 0 0 18   
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 1 0 0
-2 -3 -4 0 0 0 0 0 1 0

Tableau #5
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 -1 0 1 -1 0 0 0 0 6
0 1 1 0 1 0 0 0 0 18   
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 1 0 0 1 0 0 1 0 18   
-2 1 0 0 4 0 0 0 1 72   

Tableau #6
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 -1 0 1 -1 0 0 0 0 6
0 1 1 0 1 0 0 0 0 18   
0 -1 0 1 -1 1 0 0 0 6
0 -1 0 0 0 0 1 0 0 0
0 1 0 0 1 0 0 1 0 18   
0 -1 0 2 2 0 0 0 1 84   

Tableau #7
x₁ x₂ x₃ s1 s2 s3 s4 s5 p   
1 0 0 1 0 0 0 1 0 24   
0 0 1 0 0 0 0 -1 0 0
0 0 0 1 0 1 0 1 0 24   
0 0 0 0 1 0 1 1 0 18   
0 1 0 0 1 0 0 1 0 18   
0 0 0 2 3 0 0 1 1 102