NOT using Excel, please show all steps.

A bank is planning to install a new computerized accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates as follows: NOT using Excel, please show all steps.

Activity	Description	Predecessor	a	m	b
a	Position recruiting		5	8	17
b	System development		3	12	15
c	System training	a	4	7	10
d	Equipment training	a	5	8	23
e	Manual system test	b, c	1	1	1
f	Preliminary system changeover	b, c	1	4	13
g	Computer-personnel interface	d, e	3	6	9

h Equipment d, e 1 2.5 7

modification

i Equipment h 1 1 1

testing

j System f, g 2 2 2

debugging and

installation

k Equipment g, i 5 8 11

changeover

a. Draw the precedence diagram.

b. Determine the earliest and latest activity times, the expected completion time and standard

deviation.

c. What is the probability that the project will be completed in 40 weeks or less?

d. The following table provides the crash data for the project network. The normal activity times are

considered to be deterministic and not probabilistic.

Activity Time (weeks) Activity Cost ($)
Activity	Normal	Crash	Normal	Crash
a	9	7	4,800	6,300
b	11	9	9,100	15,500
c	7	5	3,000	4,000
d	10	8	3,600	5,000
e	1	1	0	0
f	5	3	1,500	2,000
g	6	5	1,800	2.000
h	3	3	0	0
i	1	1	0	0
j	2	2	0	0
k	8	6	5,000	7,000

Crash the network the maximum amount, indicate how much it would cost the bank, and identify the new critical path(s).