= Solution
{c}
The inequality $3y_1+y_2\ge6$, together with $y_2\ge0$, implies
$$
y_1+y_2=\frac13(3y_1+y_2)+\frac23y_2\ge2>1.
$$
Also $-y_1+y_2\ge-1$ implies
$$
-y_1+3y_2=(-y_1+y_2)+2y_2\ge-1>-5.
$$
Thus \b[both inequalities are strictly slack throughout the feasible region]. They are redundant: the remaining inequalities imply them, even with strict inequality. By <complementary slackness>, any primal optimum must therefore have $x_1=x_3=0$; this is the principle that <strictly slack dual constraints force zero primal variables>.
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