Calculate the Number of Paths, Number of Critical Paths and Project Duration

For the project network shown, the total number of paths through the network; number of critical paths; and, project duration (days) is most nearly:

a. 6; 2; and, 26 

b. 6; 1; and, 26 

c. 5; 1; and, 25

d. 3; 3; and, 24

Solution:  List the number of paths and calculate the duration for each.  

L M O R T V   = 4 + 7 + 2 + 2 + 2 + 9 = 26-days -- Critical

L M O S U     = 4 + 7 + 2 + 3 + 7 = 23-days

L M Q V      = 4 + 7 + 6 + 9 = 26-days - Critical 

L M Q U    = 4 + 7 + 6 + 7 = 24-days

L N P Q U    = 4 + 3 + 6 + 7 = 20-days

L N P Q V    = 4 + 3 + 3 + 6 + 9 = 25-days