MTH601 ASSIGNMENT NO. 1 FALL 2022 || 100% RIGHT SOLUTION || OPERATIONS RESEARCH || BY VuTech

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: 29^th 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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