Question

\[ x_{1}, x_{2}, x_{3}, x_{4} \geq 0 . \] 3. Let \( x_{0} \) be feasible solution of primal linear programming problem-lpp and \( w_{0} \) be a feasible solution of its dual, if the objective values of primal and dual lpp are equal show that \( x_{0} \) and \( w_{0} \) are the optimum solutions to the primal and dual lpp respectively. Obtain the dual linear program of the following primal linear program: \[ \begin{array}{r} \text { Minimize } z=-2 x_{1}+3 x_{2}+5 x_{3} \\ \text { Subject to } \begin{array}{r} -2 x_{1}+x_{2}+3 x_{3}+x_{4} \geq 5 \\ 2 x_{1}+. \quad x_{3}+x_{4}=6 \end{array} \\ x_{1} \leq 0, x_{2}, \quad x_{3} \geq 0 ; x_{4} \text { Unrestricted in sign. } \end{array} \]

          \[
x_{1}, x_{2}, x_{3}, x_{4} \geq 0 .
\]
3. Let \( x_{0} \) be feasible solution of primal linear programming problem-lpp and \( w_{0} \) be a feasible solution of its dual, if the objective values of primal and dual lpp are equal show that \( x_{0} \) and \( w_{0} \) are the optimum solutions to the primal and dual lpp respectively.
Obtain the dual linear program of the following primal linear program:
\[
\begin{array}{r}
\text { Minimize } z=-2 x_{1}+3 x_{2}+5 x_{3} \\
\text { Subject to } \begin{array}{r}
-2 x_{1}+x_{2}+3 x_{3}+x_{4} \geq 5 \\
2 x_{1}+. \quad x_{3}+x_{4}=6
\end{array} \\
x_{1} \leq 0, x_{2}, \quad x_{3} \geq 0 ; x_{4} \text { Unrestricted in sign. }
\end{array}
\]

x1, x2, x3, x4≥ 0 .

3. Let x0 be feasible solution of primal linear programming problem-lpp and w0 be a feasible solution of its dual, if the objective values of primal and dual lpp are equal show that x0 and w0 are the optimum solutions to the primal and dual lpp respectively.
Obtain the dual linear program of the following primal linear program:

Minimize z=-2 x1+3 x2+5 x3
Subject to
-2 x1+x2+3 x3+x4≥ 5

2 x1+. x3+x4=6

x1≤ 0, x2, x3≥ 0 ; x4 Unrestricted in sign.

Added by Arun

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