- #1
dane502
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Homework Statement
I am trying to solve the follwing linear program
<br /> \max \qquad 4x_1+x_2+3x_3<br />
<br /> \text{s.t }\qquad x_1+4x_2\qquad\,\leq1<br />
<br /> \quad\quad\quad\quad\quad\quad3x_1-x_2+x_3\leq3<br />
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):
<br /> \begin{matrix}<br /> \textcircled{1}&4&0&1&0&1\\<br /> 3&-1&1&0&1&3\\\hline<br /> -4&-2&-3&0&0&0<br /> \end{matrix}<br /> \rightarrow<br /> \begin{matrix}<br /> 1&4&0&1&0&1\\<br /> 0&-13&\textcircled{1}&-3&1&0\\\hline<br /> 0&14&-3&4&0&4<br /> \end{matrix}<br /> \rightarrow<br /> \begin{matrix}<br /> 1&\textcircled{4}&0&1&0&1\\<br /> 0&-13&1&-3&1&0\\\hline<br /> 0&-25&0&-5&3&4<br /> \end{matrix}<br /> \rightarrow<br /> \begin{matrix}<br /> 1/4&1&0&1/4&0&1/4\\<br /> 13/4&0&1&1/4&1&13/4\\\hline<br /> 25/4&0&0&5/4&3&41/4<br /> \end{matrix}<br />
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?
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