\documentclass[a4paper,12pt]{article}

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QUESTION

Draw networks for the following projects. In each case, calculate
all earliest and latest event times, and deduce the critical
path(s).

\begin{center}

\begin{tabular}{ccc}
\hline Activity&Prerequisites&Duration\\ \hline
A&-&6\\B&-&3\\C&-&5\\D&A&5\\E&B&2\\F&B&9\\G&B,C&3 \\H&D,E&6
\\I&F,G&1 \\J&F,G,H&8 \\K&I&4\\ \hline\\
\end{tabular}

\begin{tabular}{ccc}
\hline Activity&Prerequisites&Duration\\ \hline
A&-&4\\B&-&2\\C&-&3\\D&A&7\\E&C&3\\F&B,E&8\\G&D,E&3\\H&A,B,C&2\\
\hline
\end{tabular}

\end{center}


ANSWER

\begin{description}

\item[(a)]\ \\

\setlength{\unitlength}{0.5in}

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\put(3,5){\oval(.3,.3)}\put(3,5){\makebox(0,0){2}}
\put(3,3){\oval(.3,.3)}\put(3,3){\makebox(0,0){3}}
\put(3,1){\oval(.3,.3)}\put(3,1){\makebox(0,0){4}}
\put(5,4){\oval(.3,.3)}\put(5,4){\makebox(0,0){5}}
\put(5,2){\oval(.3,.3)}\put(5,2){\makebox(0,0){6}}
\put(7,4){\oval(.3,.3)}\put(7,4){\makebox(0,0){7}}
\put(7,1){\oval(.3,.3)}\put(7,1){\makebox(0,0){8}}
\put(8,3){\oval(.3,.3)}\put(8,3){\makebox(0,0){9}}

\put(1.2,3.2){\vector(1,1){1.6}}\put(1.2,3){\vector(1,0){1.6}}\put(1.2,2.8){\vector(1,-1){1.6}}
\put(3.2,4.9){\vector(2,-1){1.6}}
\put(3.2,3.2){\vector(2,1){1.6}}\put(3.2,2.9){\vector(2,-1){1.6}}
\put(3,2.8){\vector(0,-1){.4}}\put(3,2){\vector(0,-1){.4}}
\put(3.2,1.2){\vector(2,1){1.6}} \put(5.2,4){\vector(1,0){1.6}}
\put(5.2,2.3){\vector(1,1){.4}}\put(6,3){\vector(1,1){.4}}
\put(5.2,1.8){\vector(2,-1){1.6}}
\put(7.2,3.8){\vector(1,-1){.6}}\put(7,1.2){\vector(1,2){.8}}

\put(2,4.4){A,6} \put(2,3.1){B,3} \put(2,1.4){C,7}
\put(4,4.5){D,5} \put(4,3.3){E,2} \put(4,2.5){F,9}
\put(4,1.4){G,3}
\put(6,4.1){H,6}\put(6,1.5){I,1}\put(7.5,3.5){J,8}
\put(7.4,1.5){K,4}

\put(0,3.2){(0,0)} \put(3,5.3){(6,6)} \put(3,3.5){(3,8)}
\put(3,.6){(7,14)} \put(5,4.3){(11,11)} \put(5.2,2.1){(12,17)}
\put(7,4.2){(17,17)} \put(7,.6){(13,21)} \put(8.1,2.6){(25,25)}

\end{picture}

Critical path is A - D - H -J

\item[(b)]\ \\

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\put(1,3){\oval(.3,.3)}\put(1,3){\makebox(0,0){1}}
\put(3,5){\oval(.3,.3)}\put(3,5){\makebox(0,0){2}}
\put(3,3){\oval(.3,.3)}\put(3,3){\makebox(0,0){3}}
\put(3,1){\oval(.3,.3)}\put(3,1){\makebox(0,0){4}}
\put(5,4){\oval(.3,.3)}\put(5,4){\makebox(0,0){5}}
\put(7,1){\oval(.3,.3)}\put(7,1){\makebox(0,0){6}}
\put(7,5){\oval(.3,.3)}\put(7,5){\makebox(0,0){7}}
\put(8,1.7){\oval(.3,.3)}\put(8,1.7){\makebox(0,0){8}}
\put(9,4){\oval(.3,.3)}\put(9,4){\makebox(0,0){9}}

%lines from 1
\put(1.2,3.2){\vector(1,1){1.6}}\put(1.2,3){\vector(1,0){1.6}}\put(1.2,2.8){\vector(1,-1){1.6}}
%lines from 2
\put(3.2,5){\vector(1,0){3.6}}
\put(3.2,4.8){\vector(2,-1){.4}}\put(4,4.4){\vector(2,-1){.4}}
%lines from 3
\put(3.2,3.2){\vector(2,1){.4}}\put(4,3.6){\vector(2,1){.4}}
\put(3.2,2.9){\vector(4,-1){.4}}\put(4,2.7){\vector(4,-1){.4}}\put(4.8,2.5){\vector(4,-1){.4}}\put(5.6,2.3){\vector(4,-1){.4}}
\put(6.4,2.1){\vector(4,-1){.4}}\put(7.2,1.9){\vector(4,-1){.4}}
%lines from 4
\put(3.2,1.2){\vector(2,3){1.7}}\put(3.2,1){\vector(1,0){3.6}}
%lines from 5
\put(5.2,4){\vector(1,0){3.6}}
%lines from 6
\put(7,1.2){\vector(0,1){.4}}\put(7,2){\vector(0,1){.4}}\put(7,2.8){\vector(0,1){.4}}\put(7,3.6){\vector(0,1){.4}}\put(7,4.4){\vector(0,1){.4}}
\put(7.2,1.1){\vector(1,1){.4}}
%lines from 7
 \put(7.2,5){\vector(2,-1){1.6}}
%lines from 8
\put(8.2,2){\vector(1,2){.9}}

\put(2,4.4){A,4} \put(2,3.1){B,2} \put(2,1.4){C,3}
\put(5,5.1){D,7} \put(5,.7){E,3} \put(9,3){F,8} \put(8,4.7){G,3}
\put(8,3.5){H,2}

\put(0,3.2){(0,0)} \put(3,5.3){(4,4)} \put(3,3.5){(2,6)}
\put(3,.6){(3,3)} \put(5,4.3){(4,12)} \put(8.2,1.5){(6,6)}
\put(7,5.2){(11,11)} \put(7,.6){(6,6)} \put(9.1,3.6){(14,14)}

\end{picture}

There are two critical paths:   A - D - G and C - E - F.

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