For the LPP,minimize z = x_{1} + x_{2} subjec | vedclass

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(A) The constraints are $5x_{1} + 10x_{2} \geq 0$,$x_{1} + x_{2} \leq 1$,$x_{2} \leq 4$,and $x_{1}, x_{2} \geq 0$.Since $x_{1}, x_{2} \geq 0$,the cons

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There is a bounded solution

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(A) The constraints are $5x_{1} + 10x_{2} \geq 0$,$x_{1} + x_{2} \leq 1$,$x_{2} \leq 4$,and $x_{1}, x_{2} \geq 0$.Since $x_{1}, x_{2} \geq 0$,the constraint $5x_{1} + 10x_{2} \geq 0$ is always satisfied in the first quadrant.The feasible region is defined by the intersection of $x_{1} + x_{2} \leq 1$ and $x_{1}, x_{2} \geq 0$.This region is a triangle with vertices at $(0, 0)$,$(1, 0)$,and $(0, 1)$.Since the feasible region is a closed and bounded polygon,the $LPP$ has a bounded solution.

For the $LPP$,minimize $z = x_{1} + x_{2}$ subject to the constraints $5x_{1} + 10x_{2} \geq 0$,$x_{1} + x_{2} \leq 1$,$x_{2} \leq 4$ and $x_{1}, x_{2} \geq 0$.

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