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 P: 21 Two days ago I posted a similar post in the "Calculus & Beyond Forum", but I guess that this forum is more appropriate - any admin should correct me if I am wrong.. 1. The problem statement, all variables and given/known data I am trying to solve the follwing linear program $$\max \qquad 4x_1+x_2+3x_3$$ $$\text{s.t }\qquad x_1+4x_2\qquad\,\leq1$$ $$\text{ }\qquad \quad3x_1-x_2+x_3\leq3$$ 3. The attempt at a solution Using the simplex method and a tableau (negated objective function in the last row, right-hand side of constraints in the last column) $$\begin{matrix} \textcircled{1}&4&0&1&0&1\\ 3&-1&1&0&1&3\\\hline -4&-2&-3&0&0&0 \end{matrix} \rightarrow \begin{matrix} 1&4&0&1&0&1\\ 0&-13&\textcircled{1}&-3&1&0\\\hline 0&14&-3&4&0&4 \end{matrix} \rightarrow \begin{matrix} 1&\textcircled{4}&0&1&0&1\\ 0&-13&1&-3&1&0\\\hline 0&-25&0&-5&3&4 \end{matrix} \rightarrow \begin{matrix} 1/4&1&0&1/4&0&1/4\\ 13/4&0&1&1/4&1&13/4\\\hline 25/4&0&0&5/4&3&41/4 \end{matrix}$$ From which I conclude that the optimal objective value is 41/4 and the optimal solution is (0,1/4,13/4). Inserting the optimal solution in the objective function does NOT yield 41/4. It yields 10. I know from the textbook that the correct answer is 10, so my solution is correct. Can anyone explain then why my objective value in the tableau is not?