Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics IV / 5 / b / ii

The inequality $3y_1+y_2\ge 6$, together with $y_2\ge 0$, impliesAlso $-y_1+y_2\ge -1$ impliesThus 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.