Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
ME SEMESTER IV(NEW) EXAMINATION SUMMER 2017
Subject Code: 2744602 Date:03/05/2017
Subject Name: Advance Operation Research
Time: 02:30 pm to 05:00 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

What is operation research? Give features of OR. Describe briefly its applications.
07

A firm produces an alloy having the following specifications:
Specific gravity 0.98
ii) Chromium
iii) Melting point 450o C
Raw materials B and C having the properties shown in the table can be used to make an alloy. Cost of various raw materials per ton are: Rs. 90 for Rs. 280 for B and Rs. 40 for C. Formulate the LP model to find the proportions in which B and C be used to obtain an alloy of desired properties while the cost of raw material is minimum.
Property
Properties of raw material
A
B
C
Specific gravity
0.92
0.97
1.04
Chromium
7
13
16
Melting point (deg
440
490
480
07
Q.2

Solve the LP problem using graphical method.
Max. Z 2 X1 X2
Subject to constraints:
X1 2X2 10;
X1 2X2
X1 X2
X1 2X2
X1, X2
07

Solve the following LP problem using simplex method.
MIN. Z 12 X1 20 X2
Subject to constraints:
6 X1 8 X2 100;
7 X1 12 X2 120;
X1, X2
07
OR

Convert the following primal into its dual. Also write standard form of that dual and write the first matrix for initial basic solution.
Max. Z 5 X1 2 X2 3 X3
Subject to constraints:
2X1 2X2 X3
3X1 4X2
X2 3X3
X1, X2, X3
07
Q.3

Find the initial basic feasible solution to the following problem by: Least cost method and VAM. State which method is better and why?
To
Supply
1
2
3
From
1
5
1
7
10
2
6
4
6
80
3
3
2
5
15
Demand
75
20
50
07

Four machines are to be assigned to four workers. The cost of assignment is as shown below. Find the optimal assignment.
A
B
C
D
M1
15
13
14
17
M2
11
12
15
13
M3
13
12
10
11
M4
15
17
14
16
07
OR
Q.3

Give the mathematical formulation of an assignment problem. Explain how to view it in terms of an LPP problem.
07

Discuss feasible solution, infeasible solution and unbounded solution in context of LPP graphical solution with neat sketches.
07
Q.4

Solve the following game by dominance and find out the game value.
Player B
Strategy
I
II
III
IV
V
VI
Player A
I
4
2
0
2
1
1
II
4
3
1
3
2
2
III
4
3
7

1
2
IV
4
3
4

2
2
V
4
3
3

2
2
07

Solve the following 2 x n game by the method of subgames:
Player B
B1
B2
B3
Player A
A1
1
3
10
A2
7
5
2
07
OR
Q.4

Discuss the basic elements of queuing theory. Explain Kendall's notation.
07

A factory manufacturing tanks for military use has a separate tool room where special maintenance tools are stored. The average time between requirements of tool from tool room is 12 minutes and this follows the poison's distribution. Average service time of the store keeper is 10 minutes. Determine:
i. Average queue length
ii. Average length of non-empty queue
iii. Mean waiting time of a mechanic
iv. Average waiting time of mechanic who waits
07
Q.5

Define the following terms:
1. Maximal Flow Problem
2. Minimum Spanning Tree Algorithm
3. Shortest Path Problem
07

Discuss Integer linear programming. Give an example each of a pure and a mixed integer linear programming problem
07
OR
Q.5

Determine the critical path and project duration (in minutes) for given activities. Also find out floats for any four non-critical activities.
Activity
Duration
Activity
Duration
Activity
Duration
1-2
10
2-6
3
5-7
7
1-3
6
3-8
12
6-7
15
1-4
7
4-6
9
7-9
4
2-5
3
4-8
8
8-9
6
07

For the given activities (in days) determine:
Critical path using PERT.
II) Calculate variance and standard deviation for critical activities.
III) Calculate probability of completing the project in 26 days.
For z 0.7682, area 0.7782
Activity
to
tm
tp
Activity
to
tm
tp
1-2
6
9
12
3-5
1
1.5
5
1-3
3
4
11
2-6
5
6
7
2-4
2
5
14
4-6
7
8
15
3-4
4
6
8
5-6
1
2
3
07