Question

# Convert the equalities below equalities by adding sack variables. Use s_1 and s_2 for your slack variables.

Multivariable functions
Convert the equalities below equalities by adding sack variables. Use $$\displaystyle{s}_{{1}}\ \text{ and }\ {s}_{{2}}$$ for your slack variables.
$$\displaystyle{3}{x}_{{1}}+{9}{x}_{{2}}\leq{42}$$ converts to () =42
$$\displaystyle{15}{x}_{{1}}+{7}{x}_{{2}}\leq{38}$$ converts to () = 38

2021-09-18
Step 1
Solution: Given:
$$\displaystyle{3}{x}_{{1}}+{9}{x}_{{2}}\leq{42}\rightarrow{\left({1}\right)}$$
$$\displaystyle{15}{x}_{{1}}+{7}{x}_{{2}}\leq{38}\rightarrow{\left({2}\right)}$$
Now to equalize the above equation , we add $$\displaystyle{s}_{{1}}\ \text{ and }\ {s}_{{2}}$$ to the above eqn (1) and (2) respectively,
$$\displaystyle{3}{x}_{{1}}+{9}{x}_{{2}}+{s}_{{1}}={42}\rightarrow{\left({1}{a}\right)}$$
$$\displaystyle{15}{x}_{{1}}+{7}{x}_{{2}}+{s}_{{2}}={38}\rightarrow{\left({2}{f}\right)}$$
Step 2
$$\displaystyle\therefore$$ For initial simplex , basis feasible solution in $$\displaystyle{x}_{{1}}={0}\ \text{ and }\ {x}_{{2}}={0}$$
$$\displaystyle\Rightarrow{s}_{{1}}={42}\ \text{ and }\ {s}_{{2}}={38}$$
$$\displaystyle{3}{x}_{{1}}+{9}{x}_{{2}}+{s}_{{1}}={42}$$
$$\displaystyle{15}{x}_{{1}}+{7}{x}_{{2}}+{s}_{{2}}={38}$$