Gujarat Technological UniversitySummer 2024 examination

GTU 3151910 Operation Research Summer 2024 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
Illustrate graphically for Linear Programming Problem: (a) No-feasible solution (b) Unbounded solution
(b)
4 marks
A company makes two products (A and B) and both require processing on 2 machines. Product A takes 10 and 15 minutes on the two machines per unit and product B takes 22 and 18 minutes per unit on the two machines. Both the machines are available for 2640 minutes per week. The products are sold for Rs 200 and Rs 175 respectively per unit. Formulate a LP to maximize revenue? The market can take a maximum of 150 units of product 1.
(c)
7 marks
What is linear programming problem? Discuss the scope and role of LPP in solving management problems.

Q.2

14 Marks
(a)
3 marks
What are the assumptions in LPP?
(b)
4 marks

Solve following problem with graphical method. Maximize Z=3X1+9X2Z = 3X_1 + 9X_2 Subject to X1+4X2≤8X_1 + 4X_2 \le 8, X1+2X2≤4X_1 + 2X_2 \le 4 and X1,X2≥0X_1, X_2 \ge 0

(c)
7 marks

Solve the following problem using Big M method Maximize Z=4X1+5X2Z = 4X_1 + 5X_2 Subject to 2X1+3X2≤62X_1 + 3X_2 \le 6, 3X1+X2≥33X_1 + X_2 \ge 3, X1,X2≥0X_1, X_2 \ge 0.

(c)
7 marks

Using Simplex method solve the following LPP. Maximize Z=5X1+4X2Z = 5X_1 + 4X_2 Subject to X1−2X2≤1X_1 - 2X_2 \le 1, X1+2X2≥3X_1 + 2X_2 \ge 3 and X1,X2≥0X_1, X_2 \ge 0

Q.3

14 Marks
(a)
3 marks
Briefly explain about unbalanced assignment problems.
(b)
4 marks
What are trans-shipment problems? Explain with suitable example.
(c)
7 marks
Solve the following transportation problem. Obtain the initial basic feasible solution by Vogel’s method and optimal solution by MODI method.
D1D2D3D4Supply
S1324120
S2245325
S3431415
S4352640
Demand25203025
(a)
3 marks
Discuss various methods of getting IBFS in transportation problem.
(b)
4 marks

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

(c)
7 marks
Solve the following assignment problem for assigning jobs to workers.
Workers \ JobsABCD
150706080
2805070100
340706090
41004030110

Q.4

14 Marks
(a)
3 marks
Write down mathematical formula for game theory.
(b)
4 marks
Explain the queuing model as indicated by the following notations: M/D/1 : FCFS/∞/∞
(c)
7 marks
Vehicles arrive at a toll-booth at a rate of 8 per minute. The serving capacity of operator at toll-booth is 10 vehicles per minute. Find out (i) utilization factor (ii) idle time for booth operator in an 8 hour shift (iii) number of vehicles waiting in the system (iv) number of persons waiting in the queue (v) average waiting time in the queue and (vi) total time spent by a vehicle in the system
(a)
3 marks
Define the elements of Queuing system.
(b)
4 marks
What are types of strategies for game theory?
(c)
7 marks
As new automobile vehicle costs Rs. 10000 and it can be sold at the end of any year with the selling price as shown. The operating and maintenance cost are given year wise in following table. Find when the automobile vehicle needs to be replaced because of wear and tear.
Year123456
Selling Price (Rs)700060005000350025001000
Operating & Maintenance Cost (Rs)100014001600200030003500

Q.5

14 Marks
(a)
3 marks
Explain Kendall’s notation for queuing system. Also explain the terms: balking and jockeying
(b)
4 marks
Describe some important replacement situations.
(c)
7 marks
Solve the following 4 X 4 game using rule of dominance.
Player A \ Player B1234
15432
26254
31420
43532
(a)
3 marks
Differentiate between CPM and PERT
(b)
4 marks
Explain various steps involved in decision making
(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.
ActivityDurationActivityDuration
1-234-86
1-425-65
1-716-94
2-337-84
3-628-95
4-54

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About this paper

Official Gujarat Technological University (GTU) examination paper for Operation Research (Summer 2024, 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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