Question

Use the following project information:

Activity		Optimistic Time Estimate(weeks)		Most Likely Time Estimates (weeks)		Pessimistic Time Estimates (weeks)		Immediate Predecessor(s)
A		2		7		11		none
B		2		5		9		A
C		4		6		12		A
D		5		6		10		B
E		6		10		17		C
F		3		4		6		D,E
G		3		6		10		D,E
H		5		7		10		F
I		5		8		11		G
J		3		3		3		H,I

(a) Calculate the expected completion time for this project.

(Round your answer to 2 decimal places, the tolerance is +/-0.01.)

Project completion time = weeks.

(b) Identify the activities included on the critical path of this project.

(If there are several critical paths enter the first one from the alphabetical order.)

Critical activities:

ACEFHJ

ABDFHJ

ACEGIJ

ABDGIJ

.

Answer 1

EXPECTED TIME = (OPTIMISTIC TIME + (4 * MOST LIKELY TIME) + PESSIMISTIC TIME) / 6

ACTIVITY	EXPECTED TIME
A	(2 + (4 * 7) + 11) / 6 = 6.83
B	(2 + (4 * 5) + 9) / 6 = 5.17
C	(4 + (4 * 6) + 12) / 6 = 6.67
D	(5 + (4 * 6) + 10) / 6 = 6.5
E	(6 + (4 * 10) + 17) / 6 = 10.5
F	(3 + (4 * 4) + 6) / 6 = 4.17
G	(3 + (4 * 6) + 10) / 6 = 6.17
H	(5 + (4 * 7) + 10) / 6 = 7.17
I	(5 + (4 * 8) + 11) / 6 = 8
J	(3 + (4 * 3) + 3) / 6 = 3

CPM

ACTIVITY	TIME	ES	EF	LS	LF	SLACK	CRITICAL
A	6.83	0	6.83	0.00	6.83	0.00	YES
B	5.17	6.83	12.00	12.33	17.5	5.50
C	6.67	6.83	13.50	6.83	13.5	0.00	YES
D	6.50	12	18.50	17.50	24	5.50
E	10.50	13.5	24.00	13.50	24	0.00	YES
F	4.17	24	28.17	26.83	31	2.83
G	6.17	24	30.17	24.00	30.17	0.00	YES
H	7.17	28.17	35.34	31.00	38.17	2.83
I	8.00	30.17	38.17	30.17	38.17	0.00	YES
J	3.00	38.17	41.17	38.17	41.17	0.00	YES

ES = MAX(EF OF ALL PREDECESSORS); 0 FOR FIRST ACTIVITY

EF = ES + DURATION

LF = MIN(LS OF ALL SUCCESSOR ACTIVITIES); MAX EF AS LF FOR LAST ACTIVITY

LS = LF - DURATION

SLACK = LF- EF

CRITICAL PATH = LONGEST PATH WITH 0 SLACK:

CRITICAL PATH = A---C---E---G---I---J

DURATION OF PROJECT = 41.17

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