Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 7th Sem Old 171901 Operation Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (Old) EXAMINATION ? WINTER 2019
Subject Code: 171901 Date: 05/12/2019
Subject Name: Operation Research
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Discuss the scope or operation research. Also state its limitations. 07
(b) Solve the following LP problem using graphical method:
Minimize Z = 2x1 + 3x2
X1 + X2 > 6
7X1 + X2 > 14
X1 and X2 > 0
07
Q.2 (a) Solve the following LP problem using simplex method.
Minimize Z = 10X1 + 15X2 + 20X3
Subject To 2X1 + 4 X2 + 6X3 < 24
3X1 + 9X2 + 6X3 < 30
X1, X2 and X3 > 0
07
(b) Form the dual of the following primal problem.
(I) Minimize Z = 20X1 + 40X2 (I) Maximize Z = 4X1 + 10X2 +
25X3
Subject To Subject To
2X1 + 20X2 > 40 2X1 + 4X2 + 8X3 = 25
20X1 + 3X2 > 20 4X1 + 9X2 + 8X3 = 30
4X1 + 15X2 > 30 6X1 + 8X2 +2X3 = 40
X1 and X2 > 0 X1, X2 and X3, > 0
07
OR
(b) Write the difference between primal and dual in case of linear programming
Problem.
07
Q.3 (a) Consider the transportation problem shown in table
Market
1 2 3 4 5 Supply
1 10 2 16 14 10 300
Plant 2 6 18 12 13 16 500
3 8 4 14 12 10 825
4 14 22 20 8 18 375
Demand 350 400 250 150 400
Find the initial basic feasible solution using each of the following methods and
compare their total cost. a) Northwest corner method, b) least cost cell method
c) Vogel?s approximation method
07
(b) Distinguish between transportation & transshipment problems in detail. 07
OR
Q.3 (a) (Travelling salesman problem). A travelling salesman has to visit five cities. He
is to start from particular city visits each city only once and then return back to
07
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII (Old) EXAMINATION ? WINTER 2019
Subject Code: 171901 Date: 05/12/2019
Subject Name: Operation Research
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) Discuss the scope or operation research. Also state its limitations. 07
(b) Solve the following LP problem using graphical method:
Minimize Z = 2x1 + 3x2
X1 + X2 > 6
7X1 + X2 > 14
X1 and X2 > 0
07
Q.2 (a) Solve the following LP problem using simplex method.
Minimize Z = 10X1 + 15X2 + 20X3
Subject To 2X1 + 4 X2 + 6X3 < 24
3X1 + 9X2 + 6X3 < 30
X1, X2 and X3 > 0
07
(b) Form the dual of the following primal problem.
(I) Minimize Z = 20X1 + 40X2 (I) Maximize Z = 4X1 + 10X2 +
25X3
Subject To Subject To
2X1 + 20X2 > 40 2X1 + 4X2 + 8X3 = 25
20X1 + 3X2 > 20 4X1 + 9X2 + 8X3 = 30
4X1 + 15X2 > 30 6X1 + 8X2 +2X3 = 40
X1 and X2 > 0 X1, X2 and X3, > 0
07
OR
(b) Write the difference between primal and dual in case of linear programming
Problem.
07
Q.3 (a) Consider the transportation problem shown in table
Market
1 2 3 4 5 Supply
1 10 2 16 14 10 300
Plant 2 6 18 12 13 16 500
3 8 4 14 12 10 825
4 14 22 20 8 18 375
Demand 350 400 250 150 400
Find the initial basic feasible solution using each of the following methods and
compare their total cost. a) Northwest corner method, b) least cost cell method
c) Vogel?s approximation method
07
(b) Distinguish between transportation & transshipment problems in detail. 07
OR
Q.3 (a) (Travelling salesman problem). A travelling salesman has to visit five cities. He
is to start from particular city visits each city only once and then return back to
07
2
his starting point. The travelling cost of each city from a particular city is given
below. What is the sequence of his visit so that the cost is minimized?
To city
From City A B C D E
A - 3 6 2 3
B 3 - 5 2 3
C 6 5 - 6 4
D 2 2 6 - 6
E 3 3 4 6 -
(b) Alfa construction company has five crews. The skills of the crews differ from
one another because of the difference in the composition of the crews. The
company has five different projects on hand. The time (in days) taken by different
crews to complete different projects are summarized in table. Find the best
assignment of the crew to different projects such that the total time taken to
complete all the projects is minimized.
Projects
A B C D E
1 20 30 25 15 35
2 25 10 40 12 28
Crew 3 15 18 22 32 24
4 29 8 34 10 40
5 35 23 17 26 45
07
Q.4 (a) Solve the following 3 X 5 game using dominance property
Player B
1 2 3 4 5
1 2 5 10 7 2
Player A 2 3 3 6 6 4
3 4 4 8 12 1
07
(b) Define: Pay-off, saddle point, strategy, zero sum game, value of game, game
and maximin.
07
OR
Q.4 (a) A company purchases a machine for Rs 10,000. The operation cost for the
machine is expected to be more or less the same during its life. The maintenance
cost of the machine is Rs 2000 during its first year of the operation. It increases
by Rs 800 from second year to fourth year of its operation. During its fifth year
of operation, it is Rs 6000 and then onwards, it increases by Rs 1000 every year.
The interest rate is 12%. Determine the economic life of the machine.
07
(b) Explain the various elements of queuing system 07
Q.5 (a) Explain the following terms in connection with inventory management. (1) Re-
order point (2) Safety stock (3) Lead time (4) Economic lot size (5) Carrying
cost
07
(b) What is CPM and PERT. Discuss significance of using CPM and PERT. 07
OR
Q.5 (a) Explain steps in Monte Carlo simulation process. 07
(b) What is dynamic programming? Discuss the similarities between dynamic &
linear programming. How it differs from linear programming?
07
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This post was last modified on 20 February 2020