[Solved] Consider the following LP problem: max 5x_1+x_2+3x_3+4x_4 , s.t. , x_1-2x_2+4x_3+3x_4≤ 20 , -4x_1+6x_2+5x_3-4x_4≤ 40 , 2x_1-3x_2+3x_3+8x_4≤
Question: Consider the following LP problem:
\(\begin{aligned} & \max \,\,\,5{{x}_{1}}+{{x}_{2}}+3{{x}_{3}}+4{{x}_{4}} \\ & \text{s}\text{.t}\text{.} \\ & {{x}_{1}}-2{{x}_{2}}+4{{x}_{3}}+3{{x}_{4}}\le 20 \\ & -4{{x}_{1}}+6{{x}_{2}}+5{{x}_{3}}-4{{x}_{4}}\le 40 \\ & 2{{x}_{1}}-3{{x}_{2}}+3{{x}_{3}}+8{{x}_{4}}\le 50 \\ & {{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\ge 0 \\ \end{aligned}\)Use the given LP formulation and reformulate in standard form to solve using Simplex Method. If you found solution state the optimal solution, then state reason. If you found optimal solution then also state that this is the only solution, or more than one solution available, justify. If you
find that the problem has no optimal solution, then state reason why you conclude that there is no optimal solution.
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