To find the expected (estimated) time for activity \( C \), we use the PERT (Program Evaluation and Review Technique) formula for the expected time:
[tex]\[ TE = \frac{a + 4m + b}{6} \][/tex]
where
- \( a \) is the optimistic time,
- \( m \) is the most likely time, and
- \( b \) is the pessimistic time for the activity.
For activity \( C \), the given times are:
- \( a = 9 \) weeks (optimistic time),
- \( m = 12 \) weeks (most likely time),
- \( b = 18 \) weeks (pessimistic time).
Plugging these values into the PERT formula, we get:
[tex]\[ TE = \frac{9 + 4(12) + 18}{6} \][/tex]
First, calculate the values inside the parentheses:
[tex]\[ 9 + 4(12) + 18 = 9 + 48 + 18 = 75 \][/tex]
Next, divide the sum by 6:
[tex]\[ TE = \frac{75}{6} \approx 12.5 \][/tex]
Hence, the expected (estimated) time for activity [tex]\( C \)[/tex] is [tex]\( 12.5 \)[/tex] weeks.
