Solution
= Solution
The last objective row is $z+x_2+s_1+s_2=51$. Every feasible solution has nonnegative $x_2,s_1,s_2$, so $z\le51$. The displayed <basic feasible solution> has all three zero and attains 51, proving optimality. Equivalently, the resource dual prices $(1,1)$ give the same upper bound $33+18=51$ and satisfy <complementary slackness>.