Solution
= Solution
Both objectives equal $1/4$: $\mathbf1^\mathsf Tx=1/12+1/6=1/4$ and $\mathbf1^\mathsf Ty=1/6+1/12=1/4$. <Weak duality> bounds the value of every primal feasible point above by every dual feasible objective. Equality for this feasible pair therefore proves \b[both are optimal], without needing to solve either problem further.