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

Explanation:

Step1: Calculate expected time for each activity

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 \(B\): \(t_{eB}=\frac{1+4\times9+23}{6}=\frac{1 + 36+23}{6}=\frac{60}{6} = 10\)
• For \(C\): \(t_{eC}=\frac{8+4\times14+18}{6}=\frac{8+56+18}{6}=\frac{82}{6}\approx13.67\) (already given)
• For \(D\): \(t_{eD}=\frac{4+4\times6+10}{6}=\frac{4 + 24+10}{6}=\frac{38}{6}\approx6.33\)
• For \(E\): \(t_{eE}=\frac{1+4\times3+4}{6}=\frac{1+12 + 4}{6}=\frac{17}{6}\approx2.83\)
• For \(F\): \(t_{eF}=\frac{6+4\times9+21}{6}=\frac{6+36+21}{6}=\frac{63}{6}=10.5\)
• For \(G\): \(t_{eG}=\frac{3+4\times3+4}{6}=\frac{3+12+4}{6}=\frac{19}{6}\approx3.17\)
• For \(H\): \(t_{eH}=\frac{2+4\times2+2}{6}=\frac{2+8+2}{6}=\frac{12}{6}=2\)
• For \(I\): \(t_{eI}=\frac{7+4\times7+7}{6}=\frac{7+28+7}{6}=\frac{42}{6}=7\)
• 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: Determine paths and their lengths

• Path \(A - B - D - I - K\): \(9+10 + 6.33+7+1.5=33.83\)
• Path \(A - B - D - J - K\): \(9+10+6.33+8.67+1.5=35.5\)
• Path \(A - C - E - G - I - K\): \(9+13.67+2.83+3.17+7+1.5=37.17\)
• Path \(A - C - E - G - J - K\): \(9+13.67+2.83+3.17+8.67+1.5=38.84\)
• Path \(A - C - F - H - I - K\): \(9+13.67+10.5+2+7+1.5=43.67\)
• Path \(A - C - F - H - J - K\): \(9+13.67+10.5+2+8.67+1.5=45.34\)

Step3: Identify the critical path

The critical path is the longest path.

Answer:

The critical path is \(A - C - F - H - J - K\)