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OPERATIONS RESEARCH
[As per Choice Based Credit System (CBCS) scheme]
(Effective from the academic year 2017 - 2018)
SEMESTER - VI
Subject Code 17CS653
IA Marks 40
Number of Lecture Hours/Week 3
Exam Marks 60
17CS653 - OPERATIONS RESEARCH
QUESTIONS BANK
Module 3
These Questions are being framed for helping the students in the "FINAL Exams" Only (Remember for Internals the Question Paper is set by your respective teachers). Questions may be repeated, just to show students how VTU can frame Questions.
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17CS653 - OPERATIONS RESEARCH
Question Bank - MODULE - 3
1. Write the dual of the following primal LPP. (08 Marks) (Dec.2019/Jan.2020)
Max Z = 3x1 - x2 + x3
Subject to: 4x1 - x2 <= 8
8x1 + x2 + 3x3 >= 12
5x1 - 6x3 <= 13
x1, x2, x3 >= 0
2. Use dual Simplex method to solve the following LPP: (08 Marks) (Dec.2019/Jan.2020)
Max Z = -3x1 - x2
Subject to: x1 + x2 >= 1
2x1 + 3x2 >= 2
x1, x2 >= 0.
3. List out the procedural steps used to solve a LPP using dual simplex method. (08 Marks) (Dec.2019/Jan.2020)
4. Explain briefly the essence of duality theory with an example. (08 Marks) (Dec.2019/Jan.2020)
5. Write applications of dual simplex method. (06 Marks) (June/July 2019)
6. Solve by dual simplex method the following problem: (10 Marks) (June/July 2019)
Maximize Z = 2x1 + 2x2 + 4x3
Subject to constraints 2x1 + 3x2 + 5x3 >= 2
3x1 + x2 +7x3 <=3
x1 + 4x2 + 6x3 <= 5
x1, x2, x3 >= 0.
7. Construct the dual of the problem:
i. Minimize Z = 3x1 - 2x2 + 4x3 (05 Marks) (June/July 2019)
Subject to constraints 3x1 + 5x2 + 4x3 >= 7
6x1 + x2 + 3x3 >= 4
7x1 - 2x2 - x3 <= 10
x1 - 2x2 + 5x3 >= 3
4x1 + 7x2 - 2x3 >= 2
And x1, x2, x3 >= 0.
ii. Minimize Z = 3x1 + 5x2 (05 Marks) (June/July 2019)
Subject to constraints 2x1 + 6x2 <= 50
3x1 + 2x2 <= 35
5x1 - 3x2 <= 10
x2 <= 20
where x1, x2 >= 0.
8. What are the advantages of duality property? (06 Marks) (June/July 2019)
9. Use dual Simplex method to solve LPP, (08 Marks) (Dec.2018/Jan.2019)
Minimize Z = 2x1 + 2x2 + 4x3
Subject to 2x1 + 3x2 + 5x3 >= 2
3x1 + x2 + 7x3 <= 3
x1 + 4x2 + 6x3 <= 5
and x1, x2, x3 >= 0.
10. Explain the following:
i) The essence of duality theory.
ii) Primal dual relationship. (08 Marks) (Dec.2018/Jan.2019)
11. Write the procedure to solve LPP of dual Simplex method. (08 Marks) (Dec.2018/Jan.2019)
12. Write the dual of the following LPP: (08 Marks) (Dec.2018/Jan.2019)
i. Maximize Z = 3x1 - x2 + x3
Subject to 4x1 - x2 <= 8
8x1 + x2 + 3x3 >= 12
5x1 - 6x3 <= 12
And x1, x2, x3 >= 0.
ii. Minimize Z = 2x2 + 8x3
Subject to 3x1 + x2 >= 12
2x1 + x2 + 6x3 <= 6
5x1 - x2 + 3x3 =4
And x1, x2, x3 >= 0.
13. Explain the following: (06 Marks) (June/July 2018)
i) The essence of duality theory.
ii) Primal dual relationship.
14. Write the duals for the following LPP:
i) Maximize Z = x1 + 2x2 + x3
Subject to the constraint 2x1 + x2 + x3 <= 2
-2x1 + x2 - 5x3 >= -6
4x1 + x2 + x3 <= 6
And x1, x2, x3 >= 0.
ii) Maximize Z = 3x1 + 5x2 + 7x3
Subject to the constraint x1 + x2 + 3x3 <= 10
4x1 - x2 + 2x3 >= 15
And x1, x2 >= 0 and x3 is unrestricted variable. (10 Marks) (June/July 2018)
15. Give the characteristics of dual problem. (06 Marks) (June/July 2018)
16. Solve the following LPP using dual simplex method
Minimize Z = 2x1 + x2 + 3x3
Subject to x1 - 2x2 + x3 >= 4
2x1 + x2 + x3 <= 8
x1 - x3 >= 0.
With all the variables non negative. (10 Marks) (June/July 2018)
17. Explain the economic interpretation of duality with an example. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)
18. Solve the following LPP by using revises simplex method. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)
Maximize Z= x1 + 2x2
Subject to x1 + x2 <= 3
x1 + 2x2 <= 5
3x1 + x2 <= 6
And x1, x2 >= 0.
19. Explain the essence of sensitivity analysis. (05 Marks) (Dec.2017/Jan.2018| 10 Scheme)
20. Solve the following LPP by using dual simplex method.
Maximize Z = 2x1 + x2
Subject to the constrains
x1 + 2x2 <= 10
x1 + x2 <= 6
x1 - x2 <= 2
x1 - 2x2 <= 1
and x1, x2 >= 0 (15 Marks) (Dec.2017/Jan.2018| 10 Scheme)
21. Solve the following LPP by using revised Simplex method. (10 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
Maximize Z = 2x1 + x2
Subject to 3x1 + 4x2 <= 6
6x1 - x2 >= 3
Where x1, x2 >= 0
22. Explain the following terms: (i) Weak duality property(ii) Strong duality property (ii) Complimentary solution property. (06 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
23. Write the dual of the following: (10 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
i. Maximize Z = 4x1 + 10x2 + 25x3
Subject to 2x1 + 4x2 + 8x3 <= 25
4x1 + 9x2 + 8x3 <= 30
6x1 + 2x3 <= 40
Where x1, x2, x3 >= 0
ii. Minimize Z = 20x1 + 40x2
Subject to 2x1 + 20x2 >= 40
20x1 + 3x2 >= 20
4x1 + 20x2 >= 30
Where x1, x2 >= 0
24. Briefly explain about sensitivity analysis. (05 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
25. Explain primal-dual relationship with an example: (05 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
26. Solve the following by using dual simplex method.
Minimize Z = 2x1 - 2x2 + 4x3
Subject to 2x1 - 3x2 + 5x3 >= 2
3x1 + x2 - 7x4 <= 3
x1 - 4x2 + 6x3 <= 5
where x1, x2, x3 >= 0 (10 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
27. Explain the computational procedure of revised Simplex method in standard form. (08 Marks) (June/July 2017 | 10 Scheme)
28. Using revised Simplex method solve the following LPP: (12 - Marks) (June/July 2017 | 10 Scheme)
Minimize Z = x1 + x2
Subject to x1 + 2x2 >= 7
4x1 + x2 >= 6
And x1, x2 >= 0.
29. Explain the role of duality theory in sensitivity analysis. (05 Marks) (June/July 2017 | 10 Scheme)
30. Explain the procedure of dual Simplex method. (05 Marks) (June/July 2017 | 10 Scheme)
31. Use dual Simplex method and solve the following LPP and also find the solution to the primal. (10 Marks) (June/July 2017 | 10 Scheme)
Minimize Z = 2x1 + 9x2 + x3
Subject to x1 + 4x2 + 2x3 >= 5
3x1 + x2 + 2x3 >= 4
And x1, x2, x3 >= 0.
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