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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 2
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 - 2
1. Use simplex method to solve the following LPP (Linear Programming Problem). (08 Marks) (Dec.2019/Jan.2020)
Max z = 3x1 + 9x2
Subject to x1 + 4x2 <= 8
x1 + 2x2 <= 4 and
x1, x2 >= 0.
2. Solve using penalty method (Big-M) (08 Marks) (Dec.2019/Jan.2020)
Max Z = 3x1 - x2
Subject to: 2x1 + x2 >= 2
x1 + 3x2 <= 3
x2 <= 4 and
x1, x2 >= 0.
3. Obtain all the basic solutions for the system of linear equations:
2x1 + x2 + 4x3 = 11
3x1 + x2 + 5x3 = 14. (06 Marks) (Dec.2019/Jan.2020)
4. Use two phase simplex method to solve the following LPP. (10 Marks) (Dec.2019/Jan.2020)
Max Z = 5x1 - 4x2 + 3x3
Subject to 2x1 + x2 - 5x3 = 20
6x1 + 5x2 +10x3 <=76
8x1 - 3x2 + 6x3 <= 50 and
x1, x2, x3 >= 0.
5. Find all the basic solutions of the following problem:
Maximize Z = x1 + 3x2 + 3x3
Subject to constraints x1 + 2x2 + 3x3 =4
2x1 + 3x2 +5x3 = 7
Also find which of the basic solution are
i) basic feasible ii) non-degenerate basic feasible iii) optimal basic feasible. (06 Marks) (June/July 2019)
6. Solve the following LPP by Big-M method. (10 Marks) (June/July 2019)
Maximize Z = -2x1 - x2
Subject to constraints 3x1 + x2 = 3
4x1 + 3x2 >= 6
x1 + 2x2 <= 4
where x1, x2 >= 0.
7. Solve the following LPP by simplex method. (08 Marks) (June/July 2019)
Maximize = 3x1 + 2x2
Subject to constrains x1 + x2 <= 4
x1 - x2 <= 4 and
x1, x2 >= 0
8. Solve the following LPP by two-phase simplex method. (08 Marks) (June/July 2019)
Maximize z = 3x1 - x2
Subject to constraints 2x1 + x2 >= 2
x1 + 3x2 <= 2
x2 <= 4 and
x1, x2 >= 0
9. Explain the steps involved in setting up of a Simplex method. (08 Marks) (Dec.2018/Jan.2019)
10. Solve the following LPP by using Big - M method (08 Marks) (Dec.2018/Jan.2019)
Maximize Z = 4x1 + 5x2 - 3x3 +50
Subject to x1 + x2 + x3 = 10
x1 - x2 >= 1
2x1 + 3x2 + x3 <= 40 and
x1, x2, x3 >= 0.
11. Using Simplex method, solve the following LPP (08 Marks) (Dec.2018/Jan.2019)
Maximize Z = 4x1 + 3x2 + 6x3
Subject to 2x1 + 3x2 + 2x3 <= 440
4x1 + 3x3 <= 470
2x1 + 5x2 <= 430 and
x1, x2, x3 >= 0.
12. Define basic solution and obtain all the basic solutions to the following system of linear equations:
Maximize Z = x1 + 3x2 + 3x3
Subject to 2x1 + 3x2 + 4x3 = 10
3x1 + 4x2 + x3 = 12
Also classify the solutions into i) Basic Feasible Solution ii) Non-Degenerate Basic Feasible Solution iii) Optimal Basic Feasible Solution. (04 Marks) (Dec.2018/Jan.2019)
13. Write the procedure to solve LPP of two-phase Simplex method. (04 Marks) (Dec.2018/Jan.2019)
14. Define slack variable, surplus variable and basic solution. (06 Marks) (June/July 2018)
15. Solve the following LPP using simplex method. (10 Marks) (June/July 2018)
Zmax = 2x1 + 2x2 + 3x3
Subject to the constraint
2x1 + 3x2 + x3 <= 240
x1 + x2 + 3x3 <= 300
x1 + 3x2 + x3 <= 300
x1, x2, x3 >= 0.
16. Solve the following LPP by two phase method. (08 Marks) (June/July 2018)
Zmax = 3x1 - x2
Subject to constraint
2x1 + x2 >= 2
x1 + 3x2 <= 2
x2 <= 4
x1, x2 >= 0
17. Solve the following LPP by Big-M method, (08 Marks) (June/July 2018)
Maximize Z = 2x1 + 3x2 + 10x3
Subject to x1 + 2x3 = 0
x2 + x3 =1
x1, x2, x3 >= 0.
18. Explain the post optimality analysis in simplex method. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)
19. Solve the following LPP by using Big M Method. (10 Marks) (Dec.2017/Jan.2018| 10 Scheme)
Maximize Z = 6x1 + 4x2
Subject to constraints 2x1 + 3x2 <= 30
3x1 + 2x2 <= 24
x1 + x2 >= 3 and
x1, x2 >= 0.
20. Solve the following by using Big-M method. (10 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
Maximize Z = 6x1 + 4x2
Subject to 2x1 + 3x2 <= 30
3x1 + 2x2 <= 24
x1 + x2 >= 3
where x1, x2 >= 0
21. Solve the following LPP by using Two-phase Simplex method. (08 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
Maximize Z = 5x1 + 3x2
Subject to 2x1 + x2 <= 1
x1 + 4x2 >= 6
Where x1, x2 >= 0
22. Mention software packages used to solve LPP. (02 Marks) (Dec.2016/Jan.2017 | 10 Scheme)
23. Explain the setting up of simplex method. (04 Marks) Using Simplex method, (04 Marks) (June/July 2017 | 10 Scheme)
24. Solve the following LPP taking (08 Marks) (June/July 2017 | 10 Scheme)
x1 = y1 +10, x2 = y2 + 20 and x 3 = y3 +30, the LPP becomes.
Maximize Z = 10y1 + 15y2 + 8y3 +640
Subject to y1 + 2y2 + 2y3 <= 90
2y1 + y2 + y3 <= 150
3y1 + y2 + 2y3 <= 70
And y1, y2, y3 >= 0
25. Why Simplex method is better than graphical method? (03 Marks) (June/July 2017 | 10 Scheme)
26. Using Big-M method solve the following LPP: (08 Marks) (June/July 2017 | 10 Scheme)
Maximize Z = 2x1 + x2
Subject to 3x1 + x2 = 3
4x1 + 3x2 >= 6
x1 + 2x2 <= 4
x1, x2 >= 0
27. Using Two-phase method solve the LPP: (12 Marks) (June/July 2017 | 10 Scheme)
Maximize Z = -4x1 -3x2 - 9x3
Subject to 2x1 + 4x2 + 6x3 >= 15
6x1 + x2 + 6x3 >= 12
And x1, x2, x3 >= 0
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