Simple method

Problems
1.Use Simplex Method to solve
Max Z = x1 + x2 + 3x3
Subject to the constraints
3x1 + 2x2 + x3 ≤ 3
2x1 + x2 +2x3 ≤ 2
And x1, x2, x3 ≥ 0
Solution:
The standard form is
Max Z = x1 + x2 + 3x3 + 0.S1 + 0.S2
Subject to the constraints
3x1 + 2x2 + x3 + S1 = 3
2x1 + x2 +2x3 +S2 = 2
And x1, x2, x3, S1, S2 ≥ 0

As all the net evaluation, Zj – Cj are non negative, an optimum solution has been reached. Hence 
an optimum solution of the given L.P.P
x1 = 0, x2 = 0 and x3 = 1
Max Z = 3 

2.Use simplex Method to solve
Max Z = 5x1 + 3x2
Subject to the constraints
x1 + x2 ≤ 2
5x1 + 2x2 ≤ 10
3x1 + 8x2 ≤ 12
And x1, x2, ≥ 0
Solution:
The standard form is
Max Z = 5x1 + 3x2 + 0.S1 + 0.S2 + 0.x5
Subject to the constraints
x1 + x2 + S1 = 2
5x1 +2x2 +S2 = 10
3x1 + 8x2 + S3 = 12 And x1, x2, S1, S2 , S3 ≥ 0
Solution:
The standard form is 
Max Z = 5x1 + 3x2 + 0.S1 + 0.S2 + 0.x5
Subject to the constraints 
x1 + x2 + S1 = 2
5x1 +2x2 +S2 = 10
3x1 + 8x2 + S3 = 12 And x1, x2, S1, S2 , S3 ≥ 0
As all the net evaluation, Zj – Cj are non negative, an optimum solution has been reached. Hence
an optimum solution of the given L.P.P
x1 = 2, x2 = 0
Max Z = 10. 


                                     Presented By
                                     Divakar K
                                     23UCM007

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