-3
$\begingroup$

I have a question of how to make a geometric interpretation of this problem

\begin{eqnarray} \mbox{max} & z = 3x_1+x_3 \\ s.a: & \\ & \begin{array}{cc} x_1+2x_2+x_3+x_4& =10 \\ x_1-2x_2+2x_3&=6\\ 1 \leq x_1\leq 4&\\ -5 \leq x_2 \leq 4\\ 0 \leq x_3 \leq 4&\\ 0 \leq x_4 \leq 5& \end{array} \end{eqnarray}

Improve this question
$\endgroup$
  • 3
    $\begingroup$ How about solve for $x_3$ and $x_4$ explicitly (through the equality constraints), then plot the resulting inequalities as a polytope and the objective function as the level sets $\endgroup$ – Richard Jul 1 '19 at 19:23
  • 1
    $\begingroup$ The question is clear, but I have some questions about the title. What does PL stand for? Is this a misspelling of LP? Also, I am not familiar with the term "channeled variables". $\endgroup$ – Kevin Dalmeijer Jul 1 '19 at 20:02
  • $\begingroup$ "Programação linear com varíaveis canalizadas" in portuguese translates to "Linear programming with bounded with bounded variables" $\endgroup$ – Marcus Ritt Jul 2 '19 at 10:26
  • $\begingroup$ Sry, typo, only "Linear programming with bounded variables". $\endgroup$ – Marcus Ritt Jul 2 '19 at 11:23
  • 2
    $\begingroup$ Perhaps this is clear to others, but it is not clear to me what a "geometric interpretation" of an LP is. Can you clarify or provide a reference if this is an often used term? $\endgroup$ – Discrete lizard Jul 2 '19 at 11:30
5
$\begingroup$

How about this:

From the first two constraints you will cancel out $x_2$ which gives you: $2x_1 + 2x_3 + x_4 = 16$. Now, you can solve for $x_4$ and substitute that in the last constraint ($0 \le x_4 \le 5$) and you will have a system which only relies on $x_1$ and $x_3$

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.