Question:

\(\begin{aligned} & Maximize:z=2{{x}_{1}}+3{{x}_{2}}+4{{x}_{3}} \\ & subject\,\,to:{{x}_{1}}+{{x}_{2}}+{{x}_{3}}\ge 100 \\ & 2{{x}_{1}}+3{{x}_{2}}\,\,\,\,\,\le 500 \\ & {{x}_{1}}\,\,\,\,\,\,\,\,+2{{x}_{3}}\le 350 \\ & with{{x}_{1}}\ge 0,\,\,{{x}_{2}}\ge 0,\,\,{{x}_{3}}\ge 0 \\ & \\ \end{aligned}\)

a. Add slack variables or subtract surplus variables.

b. Set up the initial simplex tableau.