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如何绘制不平等区域

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如何绘制不平等区域

你能帮我画出这个不等式的区域吗：

\begin{eqnarray}
3x_1 + 3x_2 \geq 27
x_1 + 2x_2 \geq 18
4x_1 + 2x_2 \geq 28
\end{eqnarray}

我需要两个图表：一个包含三个用不同模式标记的不等式，另一个包含解的集合。

受到对另一个问题的答案的启发，我做了类似的事情：它有效，但我无法在下面写任何东西，当我尝试改变它时它只会显示解决方案，但这没有用。

\documentclass{article}     
\usepackage{pgfplots}     
\usetikzlibrary{patterns}    
\makeatletter    
\newcommand{\pgfplotsdrawaxis}{\pgfplots@draw@axis}    
\makeatother

\pgfplotsset{only axis on top/.style={axis on top=false, after end axis/.code={
             \pgfplotsset{axis line style=opaque, ticklabel style=opaque, tick style=opaque,
                          grid=none}\pgfplotsdrawaxis}}}


\newcommand{\drawge}{-- (rel axis cs:1,0) -- (rel axis cs:1,1) -- (rel axis cs:0,1) \closedcycle}

\begin{document}

\begin{figure}[htpb]     
    \centering     
    \label{fig:p3:c1}    
    \begin{tikzpicture}     
      \begin{axis}[only axis on top,    
        axis line style=very thick,     
        axis x line=bottom,     
        axis y line=left,     
         ymin=0,ymax=14,xmin=0,xmax=14,     
         xlabel=$x_1$, ylabel=$x_2$,grid=major 
      ] 

        \addplot [draw=none, pattern=vertical lines, domain=0:14]
                 {9-x} \drawge; 

        \addplot [draw=none, pattern=north west lines, domain=0:14]
                 {9-0.5*x} \drawge;
        \addplot [draw=none, pattern=horizontal lines, domain=0:14]

                 {14-2*x} \drawge; 
        \addplot[very thick, domain=0:14] {9-x};     
        \addplot[very thick, domain=0:14] {9-0.5*x};    
        \addplot[very thick, domain=0:14] {14-2*x};     
      \end{axis}     
    \end{tikzpicture}     
  \end{figure} 
\end{document}

答案1

以下是 的一种方法pstricks。我简化了不等式：

\documentclass[a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{fourier}
\pagestyle{empty}
\usepackage{array}
\usepackage[svgnames, x11names]{pstricks}%
\usepackage{pstricks-add, pst-eucl}
\usepackage{auto-pst-pdf}

\begin{document}

\everypsbox{\footnotesize}
\psset{labels=none, unit=0.25}
\psset{PointName=none, PointSymbol=none, nodesepA=-20, nodesepB=-20}
\begin{pspicture*}(-10,-10)(26,24)
    \psaxes[ticks=none]{->}(0,0)(-10,-10)(26,24)[$x_1$,-120][$x_2$,-140]
    \psset{linecolor=IndianRed}
    \pnodes{K}(-10,-10)(-10,24)(26,24)(26,-10)
    \pnodes{A}(7,0)(9,0)(18,0)
    \pnodes{B}(0,0)(0,9)(0,14)
    \uput[dl](B0){$O$}
    \pstLineAB[linecolor=IndianRed3]{A1}{B1}\uput[d](A1){9}\uput[l](B1){9}
    \pstLineAB[linecolor=Coral2]{A2}{B1}\uput[d](A2){18}
    \pstLineAB[linecolor=PeachPuff2]{A0}{B2}\uput[d](A0){7}\uput[l](B2){14}
    %%Inequalities
    \psset{linestyle=none, fillstyle=solid, opacity=0.25, framesize=15pt 5pt }
    %%1st inequality
    \pstInterLL{K0}{K1}{A1}{B1}{C}
    \pstInterLL{K0}{K3}{A1}{B1}{D}
    \pspolygon[fillcolor= IndianRed](C)(K1)(K2)(K3)(D)
    %%2nd inequality
    \pstInterLL{K0}{K1}{A2}{B1}{E}
    \pstInterLL{K2}{K3}{A2}{B1}{F}
    \pspolygon[fillcolor= Coral2](E)(K1)(K2)(K3)(F)
    %%3rd inequality
    \pstInterLL{K1}{K2}{A0}{B2}{G}
    \pstInterLL{K0}{K3}{A0}{B2}{H}
    \pspolygon[fillcolor= PeachPuff3](G)(K2)(K3)(H)
    %% Legend
    \rput(-5,-5){\setlength\arraycolsep{0.8em}$\begin{array}{@{}l l@{}}%
    \fnode*[linecolor=IndianRed](0,1.25pt){In1} & x_1 + x_2 \ge 9 \\
    \fnode*[linecolor=Coral2](0,1.25pt){In2} & x_1 + 2x_2 \ge 18\\
    \fnode*[linecolor=PeachPuff2](0,1.25pt){In2} & 2x_1 + x_2 \ge 14
    \end{array} $}
\end{pspicture*}

\end{document}

在此处输入图片描述

答案2

正如 cmhughes 指出的那样，他已经写了一个解决方案我已经适应了你的代码：

在此处输入图片描述

\documentclass{article}     
\usepackage{pgfplots}     
\usetikzlibrary{patterns,intersections}    
\makeatletter    
\newcommand{\pgfplotsdrawaxis}{\pgfplots@draw@axis}    
\makeatother

\pgfplotsset{only axis on top/.style={axis on top=false, after end axis/.code={
             \pgfplotsset{axis line style=opaque, ticklabel style=opaque, tick style=opaque,
                          grid=none}\pgfplotsdrawaxis}}}


\newcommand{\drawge}{-- (rel axis cs:1,0) -- (rel axis cs:1,1) -- (rel axis cs:0,1) \closedcycle}

\pgfplotsset{compat=1.12}
\begin{document}

\begin{figure}[htpb]     
    \centering     
    \label{fig:p3:c1}    
    \begin{tikzpicture}     
      \begin{axis}[only axis on top,    
        axis line style=very thick,     
        axis x line=bottom,     
        axis y line=left,     
         ymin=0,ymax=14,xmin=0,xmax=14,     
         xlabel=$x_1$, ylabel=$x_2$,grid=major 
      ] 

        \addplot [draw=none, pattern=vertical lines, domain=0:14]
                 {9-x} \drawge; 

        \addplot [draw=none, pattern=north west lines, domain=0:14]
                 {9-0.5*x} \drawge;
        \addplot [draw=none, pattern=horizontal lines, domain=0:14]
                 {14-2*x} \drawge; 
        \addplot[very thick, domain=0:14] {9-x};     
        \addplot[very thick, domain=0:14] {9-0.5*x};    
        \addplot[very thick, domain=0:14] {14-2*x};     
      \end{axis}     
    \end{tikzpicture}     
  \end{figure} 

\begin{figure}[htpb]     
    \centering     
    \label{fig:p3:c1}    
    \begin{tikzpicture}     
      \begin{axis}[only axis on top,    
        axis line style=very thick,     
        axis x line=bottom,     
        axis y line=left,     
         ymin=0,ymax=14,xmin=0,xmax=14,     
         xlabel=$x_1$, ylabel=$x_2$,grid=major 
      ] 

        \addplot[name path global=firstline, very thick, domain=0:14] {9-x};     
        \addplot[name path global=secondline, very thick, domain=0:14] {9-0.5*x};    
        \addplot[name path global=thirdline, very thick, domain=0:14] {14-2*x};
        %Repeat next line with a different pattern to show a pattern mixture 
        %over this region. 
        \fill[name intersections={of=secondline and thirdline, by=pointtwo}][pattern=vertical lines] (rel axis cs:0,1) -- (pointtwo)--(14,2)|-cycle;
      \end{axis}     
    \end{tikzpicture}     
  \end{figure}\end{document}

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