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You are here:Open notes-->VTU-->Sixth-Semester-BE-Degree-Examination-JuneJuly-2013-Operations-Research-Question-paper

**Sixth Semester B.E. Degree Examination, June/July 2013 Operations Research Question paper**

USN 10CSIIS661
Sixth Semester B.E. Degree Examination, June/July 2013
Operations Research
Time: 3 hrs. Max. Marks: 100
Note: Answer FWEfuli questions, selecting
at least TWO questions from each part.

**PART-A Â**

**PART-A Â**

**1)**,a.Define operations research. List and explain the various phases of an operations research (08 Marks)

**2)** a. Defme basic solution and obtain
equations:
2Xl + 3X2+ 4X3= 10, ~
3Xl + 4X2+ X3= 12 O~ ,
Also, classify the solutiQR~to

**3) **a. Write any five key relationships be ' he primal and the dual problems.

**4)** a. aoJve the following LPP by revised simplex method:
M~ . ize Z = 2xI + X2
Sub the constraints
3xI + 4X2 S; 6,
t X2S; 3
And 2:2: 0
b. Explain the fol
i) Weak dualit perty
ii) Strong duality p erty
iii) Complementary solW' ns property
iv) Complementary opti lutions prop

**Part B**

**6) **a. A company has 3 cement factories located in 3 cities X, Y and Z which supply cement to 4
project sites located in cities A, B, C and D. Each plant can supply 6, 1 and 10 truckloads of
cement daily and the daily requirements of the projects are 7, 5, 3 and 2 truckloads
respectively. The transportation cost (in thousands of rupees) per truck load of cement from
each plant to each project site are shown below.
20f3
Projects
ABC D
2 3 11 7
1 0 6 1
5 8 15 9
10CS/IS661
X
Plants y
Z
_:":>_ .• ~~,'C\~~f
'""-"''''i~
Determine the optimal distribution of the company so as to minimize the total transPQit'afi~n
cost. Use V AM method to find the initial BFS. ;!r~2)\Iarks)
Solve the following assignment problem: \¥:c~
Machines
MJ M2 M3 M4
J1 11 17 8 16
h 9 7 12 6
Jobs h 13 16 15 12
h 21 24 17 28
J5 14 19 12 11
7 a. Define the following with
i) Pay-off
ii) Zero-sum game
iii) Saddle point.
b. Solve the following game by Dorni rinciple:
II
Player A
AI 3 2 '
A2 3 4
A3 4 2
~ 0 4
ing game by graphical method:
Player B
BI B2 B3 B4
Player A AI CIIII=II}]
A2~
Write a short note on decision trees.;~.
(08 Marks)
(03 Marks)
(06 Marks)
07 Marks)
(9"J>:\arks)