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Consider the following linear programming (LP):

$\begin{array}{ll} \text{Max.} & z=2x_1+3x_2 \\ \text{Such that} & 2x_1+x_2 \leq 4 \\ & x_1 + 2x_2 \leq 5 \\ & x_1, x_2 \geq 0 \end{array}$

The optimum value of the LP is

1. $23$
2. $9.5$
3. $13$
4. $8$

ans is option 4)8  solution by graphical method

we can also eliminate options here. By adding first 2 inequalities, we get, $3x_1 + 3x_2 \leq 9$.

It can also be written as: $x_1+z \leq 9$. So, $z \leq 9\; – \;x_1$

Since, $x_1 \geq 0$, So, $z\leq 9$. So, from given options, we can eliminate first 3 options.
smart way to answer as per given options
yes. Amazing trick.