Question:

\(\begin{aligned} & Maximize:z=25{{x}_{1}}+30{{x}_{2}} \\ & subject\,\,to:3{{x}_{1}}+5{{x}_{2}}\le 47 \\ & {{x}_{1}}+{{x}_{2}}\le 25 \\ & 5{{x}_{1}}+2{{x}_{2}}\le 35 \\ & 2{{x}_{1}}+{{x}_{2}}\le 30 \\ & with{{x}_{1}}\ge 0,\,\,{{x}_{2}}\ge 0 \\ & \\ \end{aligned}\)

a. Add slack variables or subtract surplus variables.

b. Set up the initial simplex tableau.