.17 Bill Fennema, president of Fennema Construction, has developed the tasks, du

Question

.17 Bill Fennema, president of Fennema Construction,

has developed the tasks, durations, and predecessor relationships in

the following table for building new motels. Draw the AON network

and answer the questions that follow.

) What is the expected (estimated) time for activity C? 12 WEEKS

b) What is the variance for activity C? 3.36

c) Based on the calculation of estimated times, what is the critical

path?

d) What is the estimated time of the critical path?

e) What is the activity variance along the critical path?

f) What is the probability of completion of the project

eeks)

Immediate Most

Activity Predecessor(s) Optimistic Likely Pessimistic

A %u2014 4 8 10

B A 2 8 24

C A 8 12 16

D A 4 6 10

E B 1 2 3

F E, C 6 8 20

G E, C 2 3 4

H F 2 2 2

I F 6 6 6

J D, G, H 4 6 12

K I, J 2 2 3

Explanation / Answer

a) expected time of activity c = 8 + 4(12) + 16/6 =72/6 = 12 weeks

b) variance of activity c = ((16-8)/6)^2=1.78 weeks

c)

.....................path................total time

..................ABEFIK.............37.04

.................ABEGJK..............31.15

................ACFHJK...............40.14

................ACGJK...................31.48

..............ADJK........................22.81

above table shows that path A-C-F-H-J-K has a total time of 40.14

weeks. Since this is the longest duration of all the paths,

this is also our critical path for the Fennema Construction

project.

d) estimated time on criticalpath is 40.14 weeks

e)activity variance = 1 + 1.78 + 5.44 + 1.78 +0.03 = 10.03 weeks

f)standard deviation = sqrt(10.03) = 3.17 weeks

Using this we can determine the standard deviation and

probability that Fennema Construction will complete the construction of a new motel within 36 weeks.

z= (36-40.17)/3.17 = -1.32

Now we use our standard deviation of -1.32 on a normal distribution table.

By moving the Z to -1.32 on

the table we get a 9.3% chance of completing the project within 36 weeks

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