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Expert: - 3/9/2010


Question
please give the answers for following
1)Find out the optimal solution of the following LP problem through SIMPLEX method.
Maximise Z = 20x1  + 6 x2  + 8 x 3
Subject to
8 x1   +  2 x2   +  3 x3    ≤  200
4 x1  +   3 x2                               ≤  150
2 x1                           +   x3         ≤     50
x1 ,  x2   and x3                      >  0

2)Write dual of the problem given in Q.1. Explain the significance of dual variable in any LP problem.

Answer

LP Problem
To solve LP (linear programming) problems, use a simplex tableau.
That is, take the constants of each factor and make a matrix out of them.
The z row is -20 -6 -8 0 0 0 .
The 0 0 0 is one 0 for each slack variable.
There is one slack variable per equation to make the <= into an =.

The dual is found by flipping the matrix around.
Thus, the new z row is -200 -150 -50 0 0 0.
There are three slack variables in the dual problem since there are three variables here.
Below the -200 would be 8 2 3.
Below the -150 would be 4 3 0.
Below the -50 would be 2 0 1.

I have included the solution to the original problem in the attachment.

Scott A Wilson

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