MTH601 Practice Questions Solution

Q1. Find the critical path and the expected duration of the following project.

Solution

There are 7 possible paths to get from the starting point at node 1 and travel through the network to end at node 8.

1-2-3-5-7-8=A-C-E-H-K=5+11+7+6+3=32

1-2-3-5-6-8=A-C-E-I-J=5+11+7+5+8=36 1-3-5-7-8=B-E-H-K=7+7+6+3=23

1-3-5-6-8=B-E-I-J=7+7+5+8=27 1-4-5-6-8=D-F-I-J=3+9+5+8=25

1-4-5-7-8=D-F-H-K=3+9+6+3=21 1-4-6-8=D-G-J=3+12+8=23

Hence the critical path is the longest distance with the shortest possible time i.e. =1-2-3-5-6-8

=A-C-E-I-J =5+11+7+5+8

=36 I(5) A(5) C(11)

D(3) B(7) E(7) H(6)

K(3)

G(12) J(8) LST=LFTDuration of the activity

•  1-2-5-8-9=2+4+1+3=10
•  1-3-7-8-9-=2+5+4+3=14
•  1-3-6-9=2+8+5=15
•  1-4-6-9=1+3+5=9

Hence 1-3-6-9 is the critical path with duration 15.

Q4. A small marketing project consists of the jobs as shown in the table below.

Activity

X Y Z X

a) Draw the Network diagram. b) Calculate the following time estimates.

•  Earliest Start Time of each activity
•  Earliest Finish Time of each activity
•  Latest Start Time of each activity

Latest Finish Time of each activity

1. Critical Path and its duration.
2. Find Total Float, Independent Float and free Float for each activity.

Solution

a) Network:

Z(6) X(4)

Y(5)