1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
PDDC SEMESTER-VII EXAMINATION WINTER 2018
Subject Code:X71903 Date: 26/11/2018
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

Explain the characteristics of Operation Research and also state the advantages of using OR methods for problem solving.
07

Solve the following problem by graphical method:
Maximize Z 80X1 120X2
Subject to
X1 X2 9
X1 2
X2 3
20X1 50X2 360
X ,X2 0
07
Q.2

Solve the following problem by simplex method:
Maximize Z 7X1 14X2
Subject to
3X1 2X2 36
X1 4X2 10
X ,X2 0
07

Write the dual of the following Linear Programming Problem:
Maximize Z 3X1 4X2 7X3
Subject to
X1 X2 X3 10
4X1 X2- X3 15
X1 X2 X3 7
X ,X2 0 X3 unrestricted
07
OR

What is meant by unbalanced transportation problem? Explain the method for solving such a problem.
07
2
Q.3

Solve the transportation problem to minimize the transportation cost. Use Vogel's approximation method(VAM) to obtain initial basic feasible solution and MODI method for optimal solution. Is the solution unique?why?
Origin
D1
D2
D3
D4
D5
Supply
O1
12
4
9
5
9
55
O2
8
1
6
6
7
45
O3
1
12
4
7
7
30
O4
10
15
6
9
1
50
Demand
40
20
50
30
40
07

Explain the various elements of queuing system.
07
OR
Q.3

Determine an intial basic feasible solution to the following transportation problem by using Least cost method(LCM) and North west corner method.
Source
D1
D2
D3
D4
Supply
A
11
13
17
14
250
B
16
18
14
10
300
C
21
24
13
10
400
Demand
200
225
275
250
07

What is simulation? Describe the simulation process. What are the advantages and disadvantages of simulation process.
07
Q.4

ABC company is engaged in manufacturing five brands of packed snacks.It has five manufacturing set ups, each capable of manufacturing any of its brands one at a time. The cost to make a brand on these set ups vary according to the following table:
Set up
Brands
S1
S2
S3
S4
S5
B1
4
6
7
5
11
B2
7
3
6
9
5
B3
8
5
4
6
9
B4
9
12
7
11
10
B5
7
5
9
8
11
Find the optimum assignment of products on these setups resulting in the minimum cost.
07

Solve the following game using principle of dominance and obtain the optimal strategies for each player and the value of the game.
Player B
B1
B2
B3
B4
B5
B6
Player
A
A1
4
2
0
2
1
1
A2
4
3
1
3
2
2
A3
4
3
7

1
2
A4
4
3
4

2
2
A5
4
3
3

2
2
07
3
OR
Q.4

An electro mechanical equipment has a purchase price of Rs 7000/-. Its running costs per year and resale values are given in the table below:
Year
1
2
3
4
5
6
7
8
Running
Cost(Rs)
2000
2100
2300
2600
3000
3500
4100
4600
Resale value(Rs)
4000
3000
2200
1600
1400
700
700
700
Find the optimum period for the replacement.
07

Explain clearly the different costs that are involved in the inventory problem.
07
Q.5

Solve the following game using graphical method and obtain optimum strategies for player A and Player B and value of the game.
Player B
B1
B2
B3
B4
B5
Player
A
A1
2

6

5
A2

4

1
0
07

For a small project of 12 activities, the details are given in table below. Draw the network and find the critical path and project completion time.
Activity
A
B
C
D
E
F
G
H
I
J
K
L
Immediate
Predecessors



B,C
A
C
E
E

E
I,J
G
Duration (days)
9
4
7
8
7
5
10
8
6
9
10
2
07
OR
Q.5

State the rules for constructing project network and also explain with sketch, merge and burst events.
07

Explain the Dynamic problem. How is it different from Linear programming problem(LPP)? Also give some examples where dynamic problem may be used.
07