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 UniversityWinter 2023 examination

GTU 3151910 Operation Research Winter 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 10:30 AM – 1:00 PM
Questions: 5 with internal choice

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Q.1

14 Marks

(a)

3 marks

What is Operation Research? Discuss the scope of operation research in brief.

(b)

4 marks

Explain how and why operation research have been valuable in adding executive decision

(c)

7 marks

A pen manufacturer has two models. A basic model (A) and a standard model (B). Each pen of type B takes twice as long as one of type A and the company would have time to make a maximum of 2000 pen per day if only the basic model A is produced. Supply of plastic is sufficient to produce 1500 pen per day both A and B combined. The standard version of pen B requires additional accessories of which there are 600 set per day available. If the company makes a profit of Rs 3 and Rs 5 per pen of type A and B respectively, how many pens of type A and B each will have to be produced to maximize the profit?

Q.2

14 Marks

(a)

3 marks

Explain the relationship between stages and states in dynamic programming

(b)

4 marks

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

(c)

7 marks

A manufacturing company produce two product A and B. Each product undergoes through operation on machine X and Y. The time required to perform these operations with the available capacity of machines X and Y in a given quarter are given below. The market survey has predicted that not more than 450 units of product A and not more than 250 of product B can be sold in the given quarter. The company wants to determine the product mix to maximize profit. The unit profits for product A and B are Rs 20 and Rs 40 respectively. Formulate the problem and solve graphically.

Machine	Product A: time required per unit	Product B: time required per unit	Available capacity (Hrs)
X	1.5 Hrs.	1 Hrs.	750
Y	1 Hrs.	3 Hrs.	900
Profit	Rs 20	Rs 40

(c)

7 marks

Minimize $z = 3x_1 + 5x_2$ Subject to $4x_1 + 2x_2 \le 12$ , $2x_1 + 2x_2 = 10$ , $2x_1 + 5x_2 \ge 10$ Use Big-M method to solve the LPP.

Q.3

14 Marks

(a)

3 marks

What do you understand by a balanced and unbalanced transportation problem? How unbalanced problem is tackled?

(b)

4 marks

Explain the steps in volved in Modified Distribution method

(c)

7 marks

A captain of cricket team has to allot five middle order batting position to five batsmen. The average runs scored by each batsman at this position are given in table. Make the assignment so that the expected total average runs scored by these batsmen are maximum.

Batsman \ Batting Position	III	IV	V	VI	VII
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 difference between a transportation problem and an assignment problem.

(b)

4 marks

Describe the mathematical formulation of an assignment problem.

(c)

7 marks

Manufacturing firm has three plant A, B and C and three ware house P, Q and R. Their plants capacities and ware house demand and transportation cost per unit is shown in table. Find the most economical shipment to minimize the total transportation costs. There is no condition any plant can transport the product to any ware house.

From \ To	P	Q	R	Capacity
A	11	9	6	40
B	12	14	11	50
C	10	8	10	40
Demand	55	45	30	130

Q.4

14 Marks

(a)

3 marks

What is strategy? Explain the difference between pure and mixed strategy.

(b)

4 marks

Customer arrives at barber’s shop according to poisson process with a mean inter arrival time of 20 minutes. Customer spend an average time of 15 minutes in the barber’s chair. (1) What is the probability that a new arrival need not to wait for the barber to be free? (2) What is the expected number of customers in the barber’s shop? (3) How much time can a customer expect to wait for his turn? (4) How much time can a customer expect to spend in the shop?

(c)

7 marks

A manufacturer, find from his past records that the costs per year associated with a machine with a purchase price of Rs 50,000 are as given below: Determine the optimum policy.

Year	1	2	3	4	5	6	7	8
Running cost Rs (Maintenance Cost)	15000	16000	18000	21000	25000	29000	34000	40000
Scrap Value	35000	25000	17000	12000	10000	5000	4000	4000

(a)

3 marks

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

(b)

4 marks

Describe kendell’s notation in respect of queuing theory

(c)

7 marks

Assume that present value of one rupee to be spent in a year’s time is Rs 0.90 and capital cost of equipment is Rs 6000. Running costs are given in the table: When should the machine be replaced?

Year	1	2	3	4	5	6	7
Running Cost	1000	1200	1600	2000	2600	3200	4000

Q.5

14 Marks

(a)

3 marks

Explain various steps involved in decision making.

(b)

4 marks

Differentiate between CPM and PERT

(c)

7 marks

A project schedule has the following characteristic:

Construct a network diagram and find critical path, total duration of the project, various time estimates.

Activity	Duration	Activity	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
4-5	4

(a)

3 marks

What is the difference between decision making under certainty, under uncertainty and under risk

(b)

4 marks

Define: Activity, Event, Dummy activity, Float

(c)

7 marks

A small project is composed of 7 activities whose time estimates are listed in the below table. Activities are identified by their beginning and ending nodes.

1Draw Project Network

2Find the expected duration and variance for each activity

3What is the expected project length and standard deviation?

4What is the probability that the project will be completed 3 weeks later than the expected time?

Time estimates (weeks)	1-2	1-3	1-4	2-5	3-5	4-6	5-6
Optimistic	1	1	2	1	2	2	3
Most Likely	1	4	2	1	5	5	6
Pessimistic	7	7	8	1	14	8	15

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About this paper

Official Gujarat Technological University (GTU) examination paper for Operation Research (Winter 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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