problem formulating as,
Minimizez=a+b+csubject to,a−b−c≤0a+b+c≥4a+b−c=2
After converting the simplex method(big M) form,
Minimizez=a+b+c+0s1+0s2+MA1+MA2subject to,a−b−c+s1=0a+b+c−s2+A1=4a+b−c+A2=2
Steps of every table is described after all the tables..
Table 01:
S1 has gone out from the basis and a has come in to basis.
Table 02:
Row operations:
Row#1=Row#1
Row#2=Row#2-Row#1
Row#2=Row#2-Row#1
A1 has gone out from the basis and b has come in to basis.
Table 03:
Row operations:
Row#3=Row#3/2
Row#1=Row#1+Row#3
Row#2=Row#2-Row#3*2
A2 has gone out from the basis and c has come in to basis.
Table 04:
Row operations:
Row#2=Row#2/2
Row#1=Row#1+Row#2
Row#3=Row#3
since all the Z−Cj≤0 , optimal answer is occurred.
Answer to the minimization problem is,
a=2b=1c=1Zmin=4
In all the tables,
- blue numbers (Cj) =corresponding coefficients in minimization function
- Z−Cj = basis variable coefficients multiply by each column and add them -corresponding coefficient in minimization function(blue numbers)
- Then find largest Z−Cj(green column),that variable in that column is incoming variable to basis.
- Then b column is divide by that green column and find the smallest positive number. The variable is corresponding row(yellow row) is gone out from the basis.
- Then next table is find by making row operations to make the corresponding basis variable matrix to identity matrix.
- These steps are continue until all Z−Cj≤0.
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