View Single Post

## 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..

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?
 PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor