Question: Consider the following linear programming model:

\[\begin{aligned} & \max \,\,\,20{{x}_{1}}+30{{x}_{2}}+10{{x}_{3}}+40{{x}_{4}} \\ & \text{s}\text{.t}\text{.} \\ & 2{{x}_{1}}+4{{x}_{2}}+3{{x}_{3}}+7{{x}_{4}}\le 10 \\ & 10{{x}_{1}}+7{{x}_{2}}+20{{x}_{3}}+15{{x}_{4}}\le 40 \\ & {{x}_{1}}+10{{x}_{2}}+{{x}_{3}}\le 10 \\ & {{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\in \left\{ 0,1 \right\} \\ \end{aligned}\]