task2.tex

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}

\begin{document}

\section{Graphical Time-Demand Analysis}

\begin{tikzpicture} % Scale the graph for better visibility
    \begin{axis}[
        width=15cm,
        height=15cm,
        axis lines = middle,
        grid = both,
        xlabel = {Time},
        ylabel = {Demand},
        xmin = 0, xmax = 26,
        ymin = 0, ymax = 26,
        xtick = {0, 2, 4, ..., 26}, % Label only even steps on x-axis
        ytick = {0, 2, 4, ..., 26}, % Label only even steps on y-axis
        minor x tick num = 1, % Add one minor tick between each major x-tick
        minor y tick num = 1, % Add one minor tick between each major y-tick
        legend pos = south east
    ]
        % Plot the function
        \addplot[domain=0:25, blue, thick] {x};
        \addlegendentry{Supply function $w(t) = t$}
        
        % A
        \addplot+[const plot, no marks, red, thick] coordinates {(0,2) (5, 2) (5, 4)} node[above,pos=.5,red] {$A$};
        \addplot+[dashed, no marks, red, thick] coordinates {(5, 4) (10, 4) (10, 6) (15, 6) (15, 8) (20, 8)(20, 10) (25, 10) (25, 12) (30, 12)};
      \draw[dashed, red, <-] (axis cs:5,0) -- (axis cs:5,2);  % Vertical line at x = 5


        % B
        \addplot+[const plot, no marks, orange, thick] coordinates {(0,5) (5, 5) (5, 7) (7, 7)} node[above ,pos=.4,orange] {$B$};
        \addplot+[dashed, no marks, orange, thick] coordinates {(7, 7) (7, 10) (10, 10) (10, 12) (14, 12) (14, 15) (15, 15) (15, 17) (20, 17) (20, 19) (21, 19) (21, 22) (25, 22) (25, 24) (26, 24)};
        \draw[dashed, orange, <-] (axis cs:7,0) -- (axis cs:7,7);  % Vertical line at x = 5

        % C
        \addplot+[const plot, no marks, cyan, thick, solid] coordinates {(0, 6) (5, 6) (5, 8) (7, 8) (7, 11) (10, 11) (10, 13) (14, 13) (14, 16) (15, 16) (15, 18) (17, 18)} node[above ,pos=.125,cyan] {$C$};
        \addplot+[dashed, no marks, cyan, thick] coordinates {(17, 18) (20, 18) (20, 20) (21, 20) (21, 23) (25, 23) (25, 25) (26, 25)};
        \draw[dashed, cyan, <-] (axis cs:17,0) -- (axis cs:17,18);  % Vertical line at x = 5

    \end{axis}
\end{tikzpicture}


All three tasks are schedulable since the functions of all three tasks $\omega_i(t)$ touch the supply function $\omega(t)$ before their respective deadline $d_i$ 

\end{document}