Solve the following problems using the simplex algorithm, beginning with initial
ID: 3168088 • Letter: S
Question
Solve the following problems using the simplex algorithm, beginning with initial basic variables -{all slack variables). If there is a unique optimal solution, specify the optimal solution and objective value. If there are alternative optimal solutions, list three unique optimal solutions and the optimal objective value. If the problem is unbounded, specify a feasible solution and an unbounded improving direction. Ateach iteration, show the values of each decision variables, basic variab variables. les and non-basic 1. Max 5x1 4x2 6x1 +4x2 X1 +2x2 x1 +x2 x1a2 >= 0Explanation / Answer
Part 1
Standard Form of LPP:
MAXIMIZE: 5 X1 + 4 X2 + 0 S1 + 0 S2 + 0 S3
subject to
6 X1 + 4 X2 + 1 S1 = 24
1 X1 + 2 X2 + 1 S2 = 6
-1 X1 + 1 X2 +1 S3 = 1
X1, X2, S1, S2, S3 0
Tableau 1
5
4
0
0
0
Base
Cb
X1
X2
S1
S2
S3
B
RR
S1
0
6
4
1
0
0
24
24/6 = 4
S2
0
1
2
0
1
0
6
6/1 = 1
S3
0
-1
1
0
0
1
1
1/-1 = -1
j
0
0
0
0
0
Zj
-5
-4
0
0
0
0
Entering Variable: X1
Existing Variable: S1
Tableau 2
5
4
0
0
0
B
RR
Base
Cb
X1
X2
S1
S2
S3
B
RR
X1
5
1
2 / 3
1 / 6
0
0
4
6
S2
0
0
4 / 3
-1 / 6
1
0
2
1.5
S3
0
0
5 / 3
1 / 6
0
1
5
3
j
0
10/3
5/6
0
0
20
Z
0
-2 / 3
5 / 6
0
0
Entering Variable: X2
Existing Variable: S2
Tableau 3
5
4
0
0
0
B
RR
Base
Cb
X1
X2
S1
S2
S3
X1
5
1
0
1 / 4
-1 / 2
0
3
X2
4
0
1
-1 / 8
3 / 4
0
3/2
S3
0
0
0
3 / 8
-5 / 4
1
3/2
Z
0
0
3 / 4
1 / 2
0
21
Since all the z values are more than zero, the optimal solution is reached:
X1 = 3
X2 = 3/2
Z = 21
MAXIMIZE: 5 X1 + 4 X2 + 0 S1 + 0 S2 + 0 S3
subject to
6 X1 + 4 X2 + 1 S1 = 24
1 X1 + 2 X2 + 1 S2 = 6
-1 X1 + 1 X2 +1 S3 = 1
X1, X2, S1, S2, S3 0
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