Question

The director of continuing education at Bluebird University just approved the planning for a sales training seminar. Her administrative assistant identified the various activities that must be done and their relationships to each other as shown below.

			Time Estimates
Activity	Description	Immediate Predecessor(s)	Optimistic	Most likely	Pessimistic
A	Prepare course outline	None	3	4	5
B	Identify potential teachers	None	4	6	8
C	Send potential students course outline	A	8	10	12
D	Select teacher	B	2	3	4
E	Register students	C	4	8	9
F	Select classroom	D, E	1	2	6
G	Notify students and teacher of class location	F	2	4	6

1. Draw the project network diagram
2. Identify all the paths through the network and their lengths
3. Identify all the critical activities and path. How long will the entire project take?
4. The director wants to conduct the seminar 30 days from now. What is the probability that everything will be ready in time?

Answer 1

Te = (4*Tm + To+Tp)/6

Var = [ (Tp-To)/6}²

activity	To	Tm	Tp	Te	(Var)^0.5	Var
A	3	4	5	4	0.333333	0.111111
B	4	6	8	6	0.666667	0.444444
C	8	10	12	10	0.666667	0.444444
D	2	3	4	3	0.333333	0.111111
E	4	8	9	7.5	0.833333	0.694444
F	1	2	6	2.5	0.833333	0.694444
G	2	4	6	4	0.666667	0.444444

a.

There are two paths in the diagram

ACEFG with length = 28 ( this is critical path)

BDFG with length = 15.5

Variance of the critical path = 2.388

SD of the critical path = (Var)^1/2

= 1.545

The activities on critical path are A, C, E, F, G and the duration is 28.

Probability that the project will finish before 30 days is given by

z = value in case - mean / SD

= 30-28 / 1.545 =1.294

which gives probability of 0.902