# Simplex Method Giving Right Solution, Wrong Value (REPOST)

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..

## Homework Statement

I am trying to solve the follwing linear program

$$\max \qquad 4x_1+x_2+3x_3$$
$$\text{s.t }\qquad x_1+4x_2\qquad\,\leq1$$
$$\text{ }\qquad \quad3x_1-x_2+x_3\leq3$$

## 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?