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\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\multirow[b]{2}{}{Activity} & \multicolumn{3}{|c|}{Time (weeks)} & \multirow{2}{}{\begin{tabular}{c} Immediate \\ Predecessor(s) \end{tabular}} & \multirow[b]{2}{}{Activity} & \multicolumn{3}{|c|}{Time (weeks)} & \multirow{2}{}{\begin{tabular}{c} Immediate \\ Predecessor(s) \end{tabular}} \\
\cline{2-4} \cline{7-9}
& [tex]$a$[/tex] & [tex]$m$[/tex] & [tex]$b$[/tex] & & & [tex]$a$[/tex] & [tex]$m$[/tex] & [tex]$b$[/tex] & \\
\hline
A & 6 & 9 & 12 & - & G & 3 & 3 & 5 & C \\
\hline
B & 1 & 8 & 24 & A & H & 2 & 2 & 2 & F \\
\hline
C & 9 & 14 & 18 & A & J & 6 & 8 & 14 & D, O, H \\
\hline
D & 5 & 7 & 10 & A & K & 1 & 1 & 4 & J \\
\hline
E & 1 & 3 & 4 & B & & & & & \\
\hline
F & 5 & 8 & 20 & C, E & & & & & \\
\hline
\end{tabular}

a) The expected (estimated) time for activity [tex]$C$[/tex] is [tex]$\square$[/tex] weeks. (Round your response to two decimal places)



Answer :

GinnyAnswer
To determine the expected (estimated) time for activity [tex]\( C \)[/tex], we use the Program Evaluation and Review Technique (PERT) formula:

[tex]\[ \text{Expected time} = \frac{a + 4m + b}{6} \][/tex]

where:
- [tex]\( a \)[/tex] is the optimistic time
- [tex]\( m \)[/tex] is the most likely time
- [tex]\( b \)[/tex] is the pessimistic time

For activity [tex]\( C \)[/tex]:
- [tex]\( a = 9 \)[/tex]
- [tex]\( m = 14 \)[/tex]
- [tex]\( b = 18 \)[/tex]

Substitute these values into the PERT formula:

[tex]\[ \text{Expected time} = \frac{9 + 4(14) + 18}{6} \][/tex]

Calculate step-by-step:
1. First, calculate the weighted sum of the times:
[tex]\[ 9 + 4(14) + 18 = 9 + 56 + 18 \][/tex]

2. Sum these values:
[tex]\[ 9 + 56 + 18 = 83 \][/tex]

3. Divide the sum by 6:
[tex]\[ \frac{83}{6} \approx 13.83 \][/tex]

Therefore, the expected (estimated) time for activity [tex]\( C \)[/tex] is [tex]\(\boxed{13.83}\)[/tex] weeks.

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