A company specializing in custom-engineered equipment is planning to submit a proposal to the National Aeronautics and Space Administration (NASA) to build an assembled component for a new space station that NASA plans to launch into orbit. The winning proposal will be selected on the basis of both cost and timely delivery. Also, there will be a penalty clause in the NASA contract for late delivery. The company has developed the schedule of activities that are required to produce the assembled component. The activities and precedence requirements are presented in the table below. Three time estimates (in weeks) are given for each activity: optimistic time, most likely time, and pessimistic time. (a) What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time? e f 8 h Activity Immediate predecessor b i j a b c, d d e, f f, g h, i a a a 15 20 5 Optimistic time (weeks) Most likely time (weeks) Pessimistic time (weeks) 10 17 4 10 24 16 10 14 26 23 12 8 39 24 19 24 32 35 13 10 20 PERT network diagram. 15,24,39 10,1424 5,8,11 8,1624 202632 10,12.20 f 7,1013 i 7,10,19 17,2335 (a) PERT network analysis: Activity T. Critical ES EF LS LF S a 7.11 11 15 5.44 f 26 24 1.78 2.78 What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time? weeks.

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A company specializing in custom-engineered equipment is planning to submit a proposal to the National
5.
Aeronautics and Space Administration (NASA) to build an assembled component for a new space station that NASA plans to
launch into orbit. The winning proposal will be selected on the basis of both cost and timely delivery. Also, there will be a
penalty clause in the NASA contract for late delivery. The company has developed the schedule of activities that are required
to produce the assembled component. The activities and precedence requirements are presented in the table below. Three time
estimates (in weeks) are given for each activity: optimistic time, most likely time, and pessimistic time. (a) What completion
time should the company specify in its proposal in order to be 85% sure that it will complete the project on time?
ij
Activity
Immediate predecessor
Optimistic time (weeks)
a
b
d.
h
b
e, d
d e,f f,g
h, i
a
a
a
15
8
10
20
17
4
10
Most likely time (weeks)
24
16
10
14
26
23
7
12
Pessimistic time (weeks)
39
24
19
24
32
35
13
10
20
PERT network diagram.
15,24,39
10,1424
5,913
h
5,8,11
8,1624
20.2632
10.12.20
j
7,1013
7,10,19
17,2335
(a) PERT network analysis:
Activity
T.
Critical
ES
EF
LS
LF
a
7.11
11
15
5.44
f
26
24
h
1.78
i
2.78
What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time?
Tmp=
weeks.
Transcribed Image Text:A company specializing in custom-engineered equipment is planning to submit a proposal to the National 5. Aeronautics and Space Administration (NASA) to build an assembled component for a new space station that NASA plans to launch into orbit. The winning proposal will be selected on the basis of both cost and timely delivery. Also, there will be a penalty clause in the NASA contract for late delivery. The company has developed the schedule of activities that are required to produce the assembled component. The activities and precedence requirements are presented in the table below. Three time estimates (in weeks) are given for each activity: optimistic time, most likely time, and pessimistic time. (a) What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time? ij Activity Immediate predecessor Optimistic time (weeks) a b d. h b e, d d e,f f,g h, i a a a 15 8 10 20 17 4 10 Most likely time (weeks) 24 16 10 14 26 23 7 12 Pessimistic time (weeks) 39 24 19 24 32 35 13 10 20 PERT network diagram. 15,24,39 10,1424 5,913 h 5,8,11 8,1624 20.2632 10.12.20 j 7,1013 7,10,19 17,2335 (a) PERT network analysis: Activity T. Critical ES EF LS LF a 7.11 11 15 5.44 f 26 24 h 1.78 i 2.78 What completion time should the company specify in its proposal in order to be 85% sure that it will complete the project on time? Tmp= weeks.
Expert Solution
Step 1

here is the expected times forproject completion.

expected time=Te=To+Tp+4Tm/6.

Te=expected time.

To=optimistic time.

Tp=pessimistic time.

Tm= most likely time.

expected time for A=15+11+4*8/6=8.

expeced time for B=15+39+4*24/6=25

expected time for C=8+24+4*16/6=16.

expected time for D=7+19+4*10/6=11.

expected time for E=10+24+4*14/6=15.

expected time for F=20+32+4*26/6=26.

expected time for G=17+35+4*23/6=24.

expected time for H=5+13+4*9/6=9

expected time for I=7+13+4*10/6=10.

expected time for J=10+20+4*12/6=13.

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