Q.1
14 Marks(a)
Write the characteristics of Operations Research.
(b)
Discuss the limitations of linear programming problems.
(c)
Sketch the graphical representation of: (1) Infeasible solution, (2) Redundant constraint.
Gujarat Technological UniversityWinter 2024 examination
GTU 3151910 Operation Research Winter 2024 Question Paper & PDF
B.E. · Mechanical Engineering · Semester 5 · Subject code 3151910
- 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.2
14 Marks(a)
Write the steps involved in dynamic programming.
(b)
Explain with example: (1) slack variable, (2) Artificial variable in context of simplex method for LPP.
(c)
The following diet chart shows that amount of two vitamins per unit present in two different foods. Formulate primal and dual as well as write the economic interpretation of both.
| Vitamin | Spinach | Potato | Requirement of vitamins units per day |
|---|---|---|---|
| A | 6 | 8 | 100 |
| C | 7 | 12 | 120 |
| Cost / unit of food | 12 | 20 |
OR
(c)
Find initial basic feasible solution by North-west corner method and Least cost method of following transportation problem. Also make comparative comments on obtained solutions.
| D1 | D2 | D3 | D4 | Supply | |
|---|---|---|---|---|---|
| S1 | 19 | 30 | 50 | 10 | 7 |
| S2 | 70 | 30 | 40 | 60 | 9 |
| S3 | 40 | 8 | 70 | 20 | 18 |
| Demand | 5 | 8 | 7 | 14 | 34 |
Q.3
14 Marks(a)
“Transportation problem is an special case of LPP” Justify the statement.
(b)
Explain the meaning of unbalanced situation of transportation problem using suitable example.
(c)
The supervisor has to assign five machines for operation each. The cost for each operation on each machine is as shown in table. How should supervisor allocate the machine so the total cost can minimize.
| Machine \ Operation | O1 | O2 | O3 | O4 | O5 |
|---|---|---|---|---|---|
| M1 | 10 | 3 | 3 | 2 | 8 |
| M2 | 9 | 7 | 8 | 2 | 7 |
| M3 | 7 | 5 | 6 | 2 | 4 |
| M4 | 3 | 5 | 8 | 2 | 4 |
| M5 | 9 | 10 | 9 | 6 | 10 |
OR
(a)
Write the canonical form of transportation problem.
(b)
Write the difference between transportation and assignment problems.
(c)
Customers arrive at counter manned by a single person according to a Poisson process with a mean rate of 10 per hour. The time required to serve a customer has an exponential distribution with a mean of 100 seconds. Find the average waiting time of a customer in queue and the system.
Q.4
14 Marks(a)
Classify the Queuing models.
(b)
Explain how theory of replacement we used in replacement of items whose maintenance cost varies with time.
(c)
The cost of machine is Rs 60000 and its scrap value is of Rs 1000. The maintenance costs based on past experience are as follow. Find the year of replacement for machine.
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Maintenance Cost (Rs) | 1000 | 2500 | 4000 | 6000 | 9000 | 12000 | 16000 | 20000 |
OR
(a)
Define in context of game theory: strategy, Player
(b)
Discuss the characteristics of game theory.
(c)
The estimated profit from type of crop depends on amount of rainfall as given in following table. If farmer prefer to plant only one crop then suggest best crop option under high, medium and low rainfall condition. Also write the name of decision making environment which has been considered for suggestions.
| Rainfall | Crop A (Rs) | Crop B (Rs) | Crop C (Rs) |
|---|---|---|---|
| High | 8000 | 3500 | 4500 |
| Medium | 3500 | 4500 | 5000 |
| Low | 2000 | 5000 | 3000 |
Q.5
14 Marks(a)
Define: Activity, Dummy activity
(b)
Write the procedure steps for the Hurwicz criterion.
(c)
Draw a network for following project:
| Activity | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Predecessor | - | A | A | B | B, C | E | D, F | G |
OR
(a)
Explain the term “Looping” in context of networks scheduling
(b)
Differentiate between forward and backward planning
(c)
Discuss the differences among decision under certainty, decision under risk and decision under uncertainty.
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Other Semester 5 subjects
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About this paper
Official Gujarat Technological University (GTU) examination paper for Operation Research (Winter 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.