Question

ross hopkins, president of hopkins hospitality, has developed the tasks, durations, and predecessor relationships in the following table for building new motels

a) the expected (estimated) time for activity c is 13.67 weeks (round your response to two decimal places.)
b) the variance for activity c is 2.78 weeks (round your response to two decimal places )
c) based on the calculation of the estimated times, the critical path is a - c - f - h - j - k
d) the estimated time for the critical path is □ weeks (round your response to two decimal places )

Explanation:

Step1: Calculate expected time for each activity on critical path

The formula for expected time \(t_{e}=\frac{a + 4m + b}{6}\).
For \(A\): \(t_{eA}=\frac{6+4\times9 + 12}{6}=\frac{6+36+12}{6}=\frac{54}{6}=9\)
For \(C\): \(t_{eC} = 13.67\) (given)
For \(F\): \(t_{eF}=\frac{6+4\times9+21}{6}=\frac{6 + 36+21}{6}=\frac{63}{6}=10.5\)
For \(H\): \(t_{eH}=\frac{2+4\times2+2}{6}=\frac{2+8 + 2}{6}=\frac{12}{6}=2\)
For \(J\): \(t_{eJ}=\frac{6+4\times8+14}{6}=\frac{6+32+14}{6}=\frac{52}{6}\approx8.67\)
For \(K\): \(t_{eK}=\frac{1+4\times1+4}{6}=\frac{1+4+4}{6}=\frac{9}{6}=1.5\)

Step2: Sum up expected times of activities on critical path

\(T=t_{eA}+t_{eC}+t_{eF}+t_{eH}+t_{eJ}+t_{eK}\)
\(T = 9+13.67+10.5+2+8.67+1.5\)
\(T=45.34\)

Answer:

\(45.34\)