Question

Ross Hopkins, president of Hopkins Hospitality, has developed the tasks, durations, and predecessor relationships in the following table for building new motels.

	Time (weeks )						Immediate		Time (weeks )						Immediate
Activity	a		m		b		Predecessor(s)	Activity	a		m		b		Predecessor(s)
A	44		88		1010		long dash—	G	22		33		44		C, E
B	22		99		2424		A	H	22		22		22		F
C	99		1212		1616		A	I	77		77		77		F
D	44		66		99		A	J	44		77		1212		D, G, H
E	11		22		44		B	K	11		11		44		I, J
F	55		88		2121		C, E

a) To find the expected activity time, the beta distribution weights the three time estimates as follows.

Expected Time equals StartFraction left parenthesis a plus 4 m plus b right parenthesis Over 6 EndFractionExpected Time=(a+4m+b)6

Calculate the expected (estimated) time for activity C.

Expected Time =

12.1712.17

weeks (Round your response to two decimal places.)

b) To compute the variance of activity completion time, use the following formula.

Variance equals left parenthesis StartFraction left parenthesis b minus a right parenthesis Over 6 EndFraction right parenthesis squaredVariance=(b?a)62

Calculate the variance for activity C.

Variance =

11

weeks (Round your response to two decimal places.)

Consider the AON network for the project.

font size increased by 1 Upper DD

font size increased by 1 Upper FF

font size increased by 1 Upper GG

font size increased by 1 Upper AA

font size increased by 1 Upper EE

font size increased by 1 Upper CC

font size increased by 1 Upper BB

font size increased by 1 Upper HH

font size increased by 1 Upper II

font size increased by 1 Upper KK

font size increased by 1 Upper JJ

x y graph

c) The length of the path

Upper A minus Upper B minus Upper E minus Upper F minus Upper H minus Upper J minus Upper KA ? B ? E ? F ? H ? J ? K

is

40.6740.67

weeks. (Round your response to two decimal places.)

The length of the path

Upper A minus Upper B minus Upper E minus Upper F minus Upper I minus Upper KA ? B ? E ? F ? I ? K

is

38.3438.34

weeks. (Round your response to two decimal places.)

The length of the path

Upper A minus Upper B minus Upper E minus Upper G minus Upper J minus Upper KA ? B ? E ? G ? J ? K

is

nothing

weeks. (Round your response to two decimal places.)

Answer 1

(a)

Expected activity time for 'C' = (a + 4m + b)/6 = (9+4*12+16)/6 = 12.167 weeks

(b)

Variance of activity time for 'C' = (b - a)²/36 = ((16 - 9)^2)/36 = 1.36

(c)

Activity	a	m	b	te=(a+4m+b)/6
A	4	8	10	7.67
B	2	9	24	10.33
E	1	2	4	2.17
F	5	8	21	9.67
H	2	2	2	2.00
J	4	7	12	7.33
K	1	1	4	1.50
Total				40.67

(d)

Activity	a	m	b	te=(a+4m+b)/6
A	4	8	10	7.67
B	2	9	24	10.33
E	1	2	4	2.17
F	5	8	21	9.67
I	7	7	7	7.00
K	1	1	4	1.50
Total				38.33

(e)

Activity	a	m	b	te=(a+4m+b)/6
A	4	8	10	7.67
B	2	9	24	10.33
E	1	2	4	2.17
G	2	3	4	3.00
J	4	7	12	7.33
K	1	1	4	1.50
Total				32.00