Homework Sourse6 Use the simplex method to solve the following LP model Max
6. Use the simplex method to solve the following LP model: Maximize P= 3x1+ x2 Subject to x1+3x25; x1-x21; x10; x20
Solution
Maximize P= 3x1+ x2
x1+3x25;
x1-x21;
x10;
x20
s1, s2, s3 and s4 are slack variables
Forming the tableau
Tableau #1
x1 x2 s1 s2 s3 s4 p
1 3 1 0 0 0 0 5
1 -1 0 1 0 0 0 1
1 0 0 0 -1 0 0 0
0 1 0 0 0 -1 0 0
-3 -1 0 0 0 0 1 0
Tableau #2
x1 x2 s1 s2 s3 s4 p
1 3 1 0 0 0 0 5
1 -1 0 1 0 0 0 1
-1 0 0 0 1 0 0 0
0 1 0 0 0 -1 0 0
-3 -1 0 0 0 0 1 0
Tableau #3
x1 x2 s1 s2 s3 s4 p
1 3 1 0 0 0 0 5
1 -1 0 1 0 0 0 1
-1 0 0 0 1 0 0 0
0 -1 0 0 0 1 0 0
-3 -1 0 0 0 0 1 0
Tableau #4
x1 x2 s1 s2 s3 s4 p
0 4 1 -1 0 0 0 4
1 -1 0 1 0 0 0 1
0 -1 0 1 1 0 0 1
0 -1 0 0 0 1 0 0
0 -4 0 3 0 0 1 3
Tableau #5
x1 x2 s1 s2 s3 s4 p
0 1 0.25 -0.25 0 0 0 1
1 0 0.25 0.75 0 0 0 2
0 0 0.25 0.75 1 0 0 2
0 0 0.25 -0.25 0 1 0 1
0 0 1 2 0 0 1 7
Solution : Maximum value P = 7 ; x= 2 ; y=1
