Question: Consider the following linear programming model:

\[\begin{aligned} & \max \,\,\,5{{x}_{1}}+4{{x}_{2}} \\ & \text{s}\text{.t}\text{.} \\ & 3{{x}_{1}}+4{{x}_{2}}\le 10 \\ & {{x}_{1}},{{x}_{2}}\ge 0\text{ and integer} \\ \end{aligned}\]