Write the dual of the following LPP after reducing it to canonical form.
Min Z = 3x1 + 4x2 + 3x3
Subject to
2x1+4x2 =12
5x1+3x3 ≥11
6x1+ x2 ≥ 8
x1,x2,x3≥0
The LPP is given as;
3x1 + 4x2 + 3x3 = Min Z
2x1 + 4x2 + 0x3 =12
5x1 + 0x2 + 3x3 ≥ 11
6x1+ x2 + 0x3 ≥ 8
x1 ≥ 0
x2 ≥ 0
x3 ≥ 0
We construct the matrix of coefficients for the free problem, direct problem, and forward problem and name them A, B, C respectively, where;
A =
B=
D =
To find the dual of A, we compute the transpose matrix of B and to compute the dual of B, we find the tranpose matrix of A. The dual of C is the transpose matrix of C
A dual =
B dual =
C dual =
To find dual of the problem, we maximize the objective function. Also, we have the same number of constraints in the dual problem as that of the direct problem.
A maximized objective function will contain either the inequality sign " " or " ="
Therefore, the dual LPP is given as follows;
12y1 +11y2 + 8y3 = Max Z
2y1 +5y2 + 6y3 3
4y1 + y3 4
3y2 3
y1, y2, y3 ≥ 0
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