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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Gujarat Technological UniversitySummer 2026 examination

GTU 3151910 Operation Research Summer 2026 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

Briefly explain the characteristics of Operations Research.

(b)

4 marks

Find the dual of Maximize Z = 3.X1 + 2.X2 Subject to, X1 + X2 ≥ 1 X1 + X2 ≤ 7 X1 + 2X2 ≤ 10 X2 ≤ 3 X1, X2 ≥ 0

(c)

7 marks

A firm makes two products A and B, and has a total production capacity of 9 tonnes per day. The firm has a permanent contract to supply at least 2 tonnes of A and at least 3 tonnes of B per day to another company. Each tonnes of A requires 20 machine hours of production time and each tonnes of B requires 50 machine hours of production time. The daily possible number of machine hours is 360. All the firms output can be sold and the profit made is Rs. 80 per tonnes of A and Rs. 120 per tonnes of B. Formulate the linear programming problem to maximize profit and evaluate profit using graphical method.

Q.2

14 Marks

(a)

3 marks

Explain the procedure of solving a problem using dynamic programming.

(b)

4 marks

Explain the concept of crashing in project networks. Why is it necessary?

(c)

7 marks

A project schedule has the following characteristics. 4-5 4 Construct a network diagram, determine critical path and total duration of the project. Further calculate the total float for each activities.

Activities	Duration	Activities	Duration
1-2	3	4-8	6
1-4	2	5-6	5
1-7	1	6-9	4
2-3	3	7-8	4
3-6	2	8-9	5

(c)

7 marks

The following table gives the activities in a construction project and other related information. Activity Optimistic time (day) Most likely time (day) Pessimistic time (day) Draw a PERT diagram. Evaluate the critical path and calculate total project duration. Further estimate the probability that the project will be completed in 50 days.

1-2	20	30	46
1-3	9	12	21
2-3	3	5	7
2-4	2	3	4
3-4	1	2	3
4-5	12	18	24

Q.3

14 Marks

(a)

3 marks

Describe the concept of degeneracy as it occurs in transportation problems.

(b)

4 marks

Determine initial basic feasible solution of the following transportation problem using least cost method. Plants Warehouses Capacity P Q R A 35 25 15 875 B 10 20 30 575 Demand 350 350 450

(c)

7 marks

A captain of a cricket team has to allot free middle over batting positions to five batsmen. The average runs scored by each batsman at these positions are given in the following table. Batting position III IV V VI VII Batsman Apply the appropriate optimization method to assign batting positions to batsmen so that the total average runs scored by these batsmen is maximized.

A	40	40	35	25	50
B	42	30	16	25	27
C	50	48	40	60	50
D	20	19	20	18	25
E	58	60	59	55	53

(a)

3 marks

Explain the concept of a transshipment problem and how it can be represented and solved using a transportation problem framework.

(b)

4 marks

Determine an initial basic feasible solution to the following transportation problem using VAM method. Warehouse Stores I II III IV Availability

A	7	3	5	5	34
B	5	5	7	6	15
C	8	6	6	5	12
D	6	1	6	4	19
Demand	21	25	17	17	80

(c)

7 marks

The manager of a company has to assign four jobs to three persons. The persons differ in efficiency. The estimates of the time each person would take to perform a task are given in the following matrix. Person 1 2 3 Jobs Apply the appropriate optimization method to assign jobs to persons so that the total man-hours is minimized.

I	9	26	15
II	13	27	6
III	35	20	15
IV	18	30	20

Q.4

14 Marks

(a)

3 marks

Define the following terms associated with customers waiting in queue: Reneging, Jockeying, Collusion.

(b)

4 marks

Discuss the characteristics of game theory.

(c)

7 marks

The payoff matrix for a particular competitive situation is as under:

B I II III A

I	7	6	3
II	-2	2	-3
III	5	9	7

i)Reduce the size of the game to 2 x 2 matrix by method of dominance.

ii)Determine the optimal strategies.

iii)Calculate value of the game.

(a)

3 marks

Describe the method of dealing with a non-square matrix in an assignment problem with the help of an example.

(b)

4 marks

What do you understand by zero sum with reference to game theory? Explain saddle point in brief.

(c)

7 marks

The maintenance cost and resale value per year of a machine whose purchase price is ₹ 7,000 is given in below table. Apply appropriate replacement theory to decide the year for replacement of machine. Year 1 2 3 4 5 6 7 8 Maintenance cost (₹) 900 1,200 1,600 2,100 2,800 3,700 4,700 5,900 Resale value (₹) 4,000 2,000 1,200 600 500 400 400 400

Q.5

14 Marks

(a)

3 marks

Briefly explain ‘Decision Tree'.

(b)

4 marks

The research department of Marico company has recommended to the marketing department to launch a shampoo of three different types. The marketing manager has to decide one of the types of shampoo to be launched under the following estimated pay off's for various levels of sales. What will be the marketing manager's decision if

Egg Shampoo	30	10	10
Clinic Shampoo	40	15	5
Delux Shampoo	55	20	3

i)Maximin

ii)Regret critierion are applied. Types of shampoo Estimated level of sales (units) 15000 10000 5000

(c)

7 marks

Solve the following linear programming problem using simplex method. Maximize, Z = 30.X + 20.Y Subject to 3X + Y ≤ 1500, X + Y ≤ 3000 X, Y ≥ 0

(a)

3 marks

Discuss group replacement policy with suitable example.

(b)

4 marks

A large service station has a store room from where the service mechanics take the parts for the jobs they work upon. The mechanics wait in the line to get the parts that they need. The store is manned by one attendant who can, on an average, attend 7 mechanics per hour. It is observed that, on an average, the mechanics' average arrival rate at the store room is 5 per hour. Assuming that the pattern of mechanic's arrivals is Poisson distributed and the servicing time is exponentially distributed, determine

i)the expected number of mechanics in the system.

ii)the expected number of mechanics waiting in the queue.

iii)the expected time that a mechanics has to spend in the queue,.

iv)the expected time that a mechanics spends in the system.

(c)

7 marks

Solve the following linear programming minimization problem using the two-phase method. Minimize Z = 45.X1 + 28.X2 Subject to 20.X1 + 50.X2 ≥ 3600,

80X1 + 50.X2 ≤ 6000, X1, X2 ≥ 0

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About this paper

Official Gujarat Technological University (GTU) examination paper for Operation Research (Summer 2026, 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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