### Post upcoming: Math.SE unclear dual prog

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 --- title: "My Dual Answer" date: 2019-04-26T18:01:13+02:00 categories: - math tags: - linear programming - Math.SE draft: true --- I intended to answer [김종현's problem on Math.SE]. However, the programs in the question body _aren't_ typeset in [MathJax]. As a result, I downvoted and closed this question because found it _unclear_. From the proposed dual, it seems that I _shouldn't_ interpret the primal as a linear program. Anyways, _without_ further clarifications from OP, I _found_ no reason to look at this further. Here's my intended answer: > First, you have to properly write the primal as
$$\begin{array}{ccc} a & b & c \\ \hline d & e & f \\ \hdashline g & h & i \end{array}$$
$$\begin{array}{rrrrrrrrrrrrrrr} \max \quad & z = & 3w_1 & + & 4 w_2 & + & 5w_3 & && \\ \mbox{s.t.} \quad & & w_1 & - & w_2 & & & - & \varepsilon_1 & & & & & \le 0 && \\ & & & & w_2 & - & w_3 & & & - & \varepsilon_2 & & & \le 0 && \\ & & & & & & w_3 & & & & & - & \varepsilon_3 & \le 0&& \\ & & & & & & & & 2\varepsilon_1 & + & 3\varepsilon_2 & + & 4\varepsilon_3 &\ge 1 && \\ & & w_1 & + & w_2 & + & w_3 & & & & & & & = 1, && \end{array}$$
> Your claimed dual > >
$$\begin{array}{ll} \max & \varepsilon_1 r_1 + \varepsilon_2 r_2 + \varepsilon_3 r_3 + (2\varepsilon_1 +3\varepsilon_2 + 4\varepsilon_3) r_4 + r_5 \\ \text{s.t. } & x_1 + x_5 \le 3 \\ & x_2 \le 4 \\ & x_3 \le 5 \\ & r_4, r_5 \text{ free} \end{array}$$
> > is incorrect since it's *not* a linear program. : https://web.archive.org/web/20190426160341/https://math.stackexchange.com/questions/3203415/am-i-have-right-answer-about-dual-problem : https://www.mathjax.org/
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