Solve the following problem using the Revised Simplex Algori

Solve the following problem using the Revised Simplex Algorithm
maximize z = 4x1 x2 + 3x3 + 3x4 subject to
4x1+ 2x2 + x3 + 2x4 40
2x1 x2+ 2x3 + x4 8
x1 2x2+ 4x3 + x4 10
all xj 0

Solution

Maximize z = 4x1 x2 + 3x3 + 3x4
4x1+ 2x2 + x3 + 2x4 40
2x1 x2+ 2x3 + x4 8
x1 2x2+ 4x3 + x4 10
x1 >=0
x2>=0
x3>=0
x4>=0

Solving by simplex method: forming the Tableau

Tableau #1
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
0 1 2 1 0 0 0 0 0 0 0 40   
2 2 1 0 1 0 0 0 0 0 0 8
0 4 1 0 0 1 0 0 0 0 0 10   
0 0 0 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 0 -1 0 0
-4 -3 -3 0 0 0 0 0 0 0 1 0

Tableau #2
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
0 1 2 1 0 0 0 0 0 0 0 40   
2 2 1 0 1 0 0 0 0 0 0 8
0 4 1 0 0 1 0 0 0 0 0 10   
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 0 -1 0 0
-4 -3 -3 0 0 0 0 0 0 0 1 0

Tableau #3
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
0 1 2 1 0 0 0 0 0 0 0 40   
2 2 1 0 1 0 0 0 0 0 0 8
0 4 1 0 0 1 0 0 0 0 0 10   
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 0 0 -1 0 0
-4 -3 -3 0 0 0 0 0 0 0 1 0

Tableau #4
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
0 1 2 1 0 0 0 0 0 0 0 40   
2 2 1 0 1 0 0 0 0 0 0 8
0 4 1 0 0 1 0 0 0 0 0 10   
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 0 0 -1 0 0
-4 -3 -3 0 0 0 0 0 0 0 1 0

Tableau #5
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
0 1 2 1 0 0 0 0 0 0 0 40   
2 2 1 0 1 0 0 0 0 0 0 8
0 4 1 0 0 1 0 0 0 0 0 10   
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 0 0 1 0 0
-4 -3 -3 0 0 0 0 0 0 0 1 0

Tableau #6
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
0 1 2 1 0 0 0 0 0 0 0 40   
1 1 0.5 0 0.5 0 0 0 0 0 0 4
0 4 1 0 0 1 0 0 0 0 0 10   
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 0 0 1 0 0
0 1 -1 0 2 0 0 0 0 0 1 16   

Tableau #7
x1x2 x3 x4 s1 s2 s3 s4 s5 s6 s7 z   
-4 -3 0 1 -2 0 0 0 0 0 0 24   
2 2 1 0 1 0 0 0 0 0 0 8
-2 2 0 0 -1 1 0 0 0 0 0 2
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 0 0 1 0 0 0
2 2 0 0 1 0 0 0 0 1 0 8
2 3 0 0 3 0 0 0 0 0 1 24

Optimal Solution from tableau we get : z = 24;

x1x2 = 0, x3 = 0, x4 = 8