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MTH601 ASSIGNMENT NO. 1 FALL 2022 |
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MTH601 ASSIGNMENT NO. 1 FALL 2022 || 100% RIGHT SOLUTION || OPERATIONS RESEARCH || BY VuTech
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ASSIGNMENT NO 1(MTH 601)
Maximum Marks: 20
Due Date: 29th
November, 2022
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Question No 1: Marks=10
Consider the network diagram which consists of the following
activities.
Calculate the following time estimates for each activity.
Ø Earliest
Start Time(EST)
Ø Earliest
Finish Time(EFT)
Ø Latest
Start Time(LST)
Ø Latest
Finish Time(LFT)
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Solution:
|
Activities |
Duration |
EST |
EFT=EST+D |
LST=LFT-D |
LFT |
|
0-1 |
2 |
0 |
0+2=2 |
2-2=0 |
2 |
|
1-2 |
8 |
2 |
2+8=10 |
16-8=8 |
16 |
|
1-3 |
10 |
2 |
2+10=12 |
12-10=2 |
12 |
|
2-4 |
6 |
10 |
10+6=16 |
22-6=16 |
22 |
|
2-5 |
3 |
10 |
10+3=13 |
25-3=22 |
25 |
|
3-4 |
3 |
12 |
12+3=15 |
22-3=19 |
22 |
|
3-6 |
7 |
12 |
12+7=19 |
19-7=12 |
19 |
|
4-7 |
5 |
16 |
16+5=21 |
27-5=22 |
27 |
|
5-7 |
2 |
13 |
13+2=15 |
27-2=25 |
27 |
|
6-7 |
8 |
19 |
19+8=27 |
27-8=19 |
27 |
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Question No 2: Marks=10
The time
estimates for the activity of the PERT diagram are given in the table below.
Calculate the expected time, variance and standard deviation for each activity
|
Activity |
to |
tm |
tp |
|
1-2 |
1 |
2 |
3 |
|
2-3 |
8 |
10 |
12 |
|
2-4 |
2 |
4 |
6 |
|
2-5 |
3 |
5 |
7 |
|
3-6 |
4 |
5 |
6 |
|
4-6 |
7 |
8 |
9 |
|
5-7 |
6 |
8 |
10 |
|
6-7 |
1 |
4 |
7 |
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Solution:
|
Activities |
to |
tm |
tp |
`t_e=\frac{t_o +
4t_m + t_p}{6}` |
`S.D=\frac{t_p
- t_o}{6}` |
`Variance
=(\frac{t_p - t_o}{6})^2` |
|
1-2 |
1 |
2 |
3 |
2 |
1/3 |
1/9 |
|
2-3 |
8 |
10 |
12 |
10 |
2/3 |
4/9 |
|
2-4 |
2 |
4 |
6 |
4 |
2/3 |
4/9 |
|
2-5 |
3 |
5 |
7 |
5 |
2/3 |
4/9 |
|
3-6 |
4 |
5 |
6 |
5 |
1/3 |
1/9 |
|
4-6 |
7 |
8 |
9 |
8 |
1/3 |
1/9 |
|
5-7 |
6 |
8 |
10 |
8 |
2/3 |
4/9 |
|
6-7 |
1 |
4 |
7 |
4 |
1 |
1 |
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