intersection of functions or polygon tikz?

Question

Hello I am creating a plot using tikz I have created 3 functions on a plot and took the area above each of them using drawge. My question is how I can fill the area above intersection of two functions ? or maybe I should create a polygon with the point of the intersection as one of the points of the polygon? The second part of question is why on x axis the part of the axis is transparent not black? Thank You in advance for answers

the plot looks now like this :

the picture below shows how I want it to look like

here is my current code:

\pgfplotsset{compat=newest}
\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
}
\newcommand{\drawle}{%
  -- (rel axis cs:1,1) -- (rel axis cs:1,0) -- (rel axis cs:0,0) \closedcycle
}



 \begin{tikzpicture} [scale=1.5]
 \begin{axis}[only axis on top,
axis line style=very thick, 
axis x line=bottom, 
axis y line=left, 
ymin=0,
ymax=20,
xmin=0,
xmax=20, 
xlabel=$y_1$,
ylabel=$y_2$,
grid=major, 
ytick={-5,0, 5,10,15,20},
xtick={-5,0,5,10,15,20},
  ]   
       \addplot[
  very thick,
  fill=red!10,
  domain=-5:20,
] {(29-6*x)} \drawge;  

  \addplot[
  very thick,
  fill=red!10,
  domain=-5:20,
] {(29-6*x)} \drawge;  


\addplot[
  very thick,
  fill=yellow!10,
  domain=-5:20,
    ] {(16-4*x)/2} \drawge; 

\addplot[very thick, domain=-5:20] {(24-x)/5};
  \addplot[very thick, domain=-5:20] {(29-6*x)};
\addplot[very thick, domain=-5:20] {(16-4*x)/2};
  \end{axis}
 \end{tikzpicture}

Answer 1

You don't need those extra plots, which by the way are creating weird artifacts. Therefore, I have some suggestions:

• Prefer to define a particular version for your pgfplots. If you set it to newest and then there is an update, it might break your document. Choose it manually like compat=1.13.
• Use the fillbetween pgfplots library to fill between plots and paths.
• axis line style={shorten >=-10pt}, makes the axis lines slightly longer so that you have the arrow coming out of the grid.
• x axis line style={name path=xaxis} sets the path name for the x axis.
• You can do the same with any path by writing name path=<name> in the plot/path options.
• If you want the grid to be visible, you have two ways: (1) you use regular colors but with opacity or (2) you place the grid on top (in the axis options).

Output

Code

\documentclass[margin=10pt]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=1.13}
\usepgfplotslibrary{fillbetween}

\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
    },
  },
    }

\begin{document}
\begin{tikzpicture}%[scale=1.5]
\begin{axis}[only axis on top,
axis line style=very thick, 
axis x line=bottom, 
axis y line=left, 
ymin=0,
ymax=20,
xmin=0,
xmax=20, 
xlabel=$y_1$,
ylabel=$y_2$,
axis line style={shorten >=-10pt},
grid=major, 
ytick={-5,0, 5,10,15,20},
xtick={-5,0,5,10,15,20},
x axis line style={name path=xaxis}
  ]    

\path[name path=top] (0,20) -- (20,20); % defines an invisible path at the top of the grid, could be improved.

    \addplot[very thick, name path=a, domain=0:20] {(24-x)/5};
    \addplot[very thick, name path=b, domain=0:20] {(29-6*x)};
    \addplot[very thick, name path=c, domain=0:20] {(16-4*x)/2};

\addplot[fill=red!10] fill between[
    of=b and top,
    split,
    every even segment/.style={
        fill=none
    }
];

\addplot[fill=none] fill between[
        of=a and c,
        split,
        every segment no 1/.style={
            fill=yellow!10
        }
    ];

\addplot[fill=yellow!10] fill between[
        of=b and c,
    ];

\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

Metapost is often more flexible for this sort of semi-numerical diagram. Here I've shown it wrapped up in luamplib, which requires lualatex to process.

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
% first define the 20x20 box
path box;
box = unitsquare scaled 5cm;

% now define the three lines
path m[];
m1 = point -8/20 of box -- point   4/20 of box;
m2 = point -5/20 of box -- point  21/20 of box;
m3 = point  5/20 of box -- point -21/20 of box;

% now define the two regions to be filled
path r[];
r1 = point 2 of box -- point 3 of box -- m1 -- point 1 of box -- cycle;
r2 = point 2 of box -- point 1 of m3 -- m2 intersectionpoint m3 -- point 1 of m2 -- cycle;

% fill the regions
fill r1 withcolor 0.8[red+green,white];
fill r2 withcolor 0.8[blue, white];

% draw the lines
draw m1; draw m2; draw m3;

% mark the axes
drawarrow point 0 of box -- point 1 of box scaled 1.08;
drawarrow point 0 of box -- point 3 of box scaled 1.08;

label.llft("$0$", origin);
for i = 5 step 5 until 20: 
   draw (down--up)    shifted point  i/20 of box;
   draw (left--right) shifted point -i/20 of box;
   label.bot("$" & decimal i & "$", point  i/20 of box);
   label.lft("$" & decimal i & "$", point -i/20 of box);
endfor

label("$y_1$", point 0.5 of box shifted 20 down);
label(textext("$y_2$") rotated 90, point 3.5 of box shifted 24 left);

endfig;
\end{mplibcode}
\end{document}

I note one slightly irritating wrinkle that despite having set \mplibtextextlabel you still need to explicitly add the textext() macro call if you want to apply a transformation to the resulting picture.