(a) Apply Big M method to solve the LPP Maximize w Subject to $x_{1}+x_{2}+2 x_{3} \leq 5$ $$ \begin{aligned} & 2 x_{1}+3 x_{2}+4 x_{3}=12 \\ & x_{1}, x_{2}, x_{3} \geq 0 \end{aligned} $$
Explanation
To apply the Big M method to solve the given LPP, we first convert the problem into standard form. We then apply the simplex algorithm to find the optimal solution. The optimal solution is $x_{1} = 0, x_{2} = 0, x_{3} = 3$ and the maximum value of $w$ is $w = 12$.
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