Question: Solve the problem using Lagrange multiplier method Minimize $f=3 x_{1}^{2}+4 x_{2}^{2}+x_{1} x_{3}+x_{2} x_{3}$ subject to [begin{aligned}& x_{1}+3 x_{2}=3 & 2 x_{1}+x_{3}=7end{aligned}]

Solve the problem using Lagrange multiplier method

Minimize $f=3 x_{1}^{2}+4 x_{2}^{2}+x_{1} x_{3}+x_{2} x_{3}$

subject to

\[\begin{aligned}& x_{1}+3 x_{2}=3 \\& 2 x_{1}+x_{3}=7\end{aligned}\]

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