What is the exam pattern and passing mark for GTU Operation Research (3151910)?

The GTU theory examination carries 70 total marks with a duration of 2.5 Hours. Minimum passing criteria is 23 marks (33%). The paper consists of 5 main questions with official marking breakdown and internal choices.

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The official GTU question paper PDF is linked directly from Gujarat Technological University's official examination archive. You can view the full paper online or download the original file.

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Gujarat Technological UniversitySummer 2023 examination

GTU 3151910 Operation Research Summer 2023 Question Paper & PDF

B.E. · Mechanical Engineering · Semester 5 · Subject code 3151910

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Total: 70 marks
To pass: 23 marks (33%)
Duration: 2.5 Hours 2:30 PM – 5:00 PM
Questions: 5 with internal choice

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Q.1

14 Marks

(a)

3 marks

Define OR. Discuss the origin and development of OR.

(b)

4 marks

Discuss Various phases in solving an OR problems.

(c)

7 marks

Explain the Scope of OR in the various sectors.

Q.2

14 Marks

(a)

3 marks

What are the applications of LPP?

(b)

4 marks

Define: (I) Basic Feasible Solution (II) Objective Function (III) Degenerate Solution (IV) Optimal Feasible Solution

(c)

7 marks

Solve the following LPP by Simplex Method. Maximize $Z = 70x_1 + 150x_2$ Subject to $4x_1 + 6x_2 \le 84$ , $0.5x_1 + x_2 \le 60$ and $x_1, x_2 \ge 0$

(c)

7 marks

Find dual of the following LPP:

Minimize $Z = 5x_1 - 6x_2 + 4x_3$ Subject to $3x_1 + 4x_2 + 6x_3 \ge 9$ , $x_1 + 3x_2 + 2x_3 \ge 5$ , $7x_1 - 2x_2 - x_3 \le 10$ and $x_1, x_2, x_3 \ge 0$

Q.3

14 Marks

(a)

3 marks

How will you define transportation problem? Give mathematical statement of problem explaining each term.

(b)

4 marks

Discuss various methods of getting IBFS in transportation problem.

(c)

7 marks

Find out optimal solution for following transportation problem.

	1	2	3	4	5	6	Supply
A	9	12	9	6	9	10	50
B	7	3	7	7	5	5	60
C	6	5	9	11	3	11	20
D	6	8	11	2	2	10	90
Demand	40	40	60	20	40	20	220

(a)

3 marks

Define: (I) Discount Rate (II) Money Value (III) Present worth factor

(b)

4 marks

Discuss about the individual replacement versus group replacement.

(c)

7 marks

A printer costing Rs. 6500 initially has maintenance & resale value as given below:

Year (n)	1	2	3	4	5	6	7
Resale Value (s)	3000	2500	2000	1500	1000	700	500
Maintenance cost F (t)	100	250	500	1000	1500	1800	2000

Q.4

14 Marks

(a)

7 marks

A postman has to visit four societies of an area. He does not want to visit any society twice before completing the visit of all societies from starting one. Following is the matrix showing distance (in kms) of his journey. Suggest him such that his constraint is fulfilled as well as it takes least time.

	I	II	III	IV
I	-	0.420	0.920	0.620
II	0.520	-	1.520	0.420
III	0.520	0.620	-	0.320
IV	0.820	0.920	1.420	-

(b)

7 marks

Solve the following assignment problem for assigning jobs to workers.

Workers \ Jobs	A	B	C	D
1	50	70	110	60
2	80	50	90	60
3	40	70	100	70
4	100	40	80	30

(a)

3 marks

Define the elements of Queuing system.

(b)

4 marks

Explain Kendal’s notation for Queuing system.

(c)

7 marks

At barber’s shop, the customers arrive at the average interval of 6 minutes, and the barber takes on an average 5 minutes for serving the person. Calculate: (1) Counter utilization level (2) Average number of customers in the including at service system (3) Average number of customers in the queue (4) Average waiting time of customers in the system (5) Expected average waiting time in the queue

Q.5

14 Marks

(a)

3 marks

Write down mathematical formula for game theory.

(b)

4 marks

What are types of strategies for game theory?

(c)

7 marks

Solve the following pay-off matrix for player A. Also find out the optimal strategies and value of the game using algebraic method.

Player A \ Player B	B1	B2	B3
A1	275	-50	-75
A2	125	130	150

(a)

3 marks

Define: (I) Event (II) Activity (III) Total float with respect to CPM/PERT

(b)

4 marks

Explain term “Crashing of network”. Why it is required?

(c)

7 marks

The activities A to H for a new project having relationships and timings shown in table below. Relation between activities: A

1Draw the network.

2Find the critical path & expected time of completion of the project.

3What will be the standard deviation of the project completion duration?

4What will be the probability of completing the project in expected time of completion?

Duration (in days):

Activity	$t_o$	$t_m$	$t_p$
A	2	2	8
B	2	5	8
C	3	6	15
D	2	5	14
E	1	1	7
F	2	2	8
G	2	2	8
H	2	5	14

More Operation Research papers

Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.

Summer 202670 marks · 5 questions

Winter 202570 marks · 5 questions

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Other Semester 5 subjects

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2151908

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About this paper

Official Gujarat Technological University (GTU) examination paper for Operation Research (Summer 2023, B.E. · Mechanical Engineering, Sem 5). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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