Hall Ticket No Question Paper Code: AHS012
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Four Year B.Tech V Semester End Examinations (Regular) November, 2018
Regulation: IARE R16
OPTIMIZATION TECHNQUES
Time: 3 Hours (Common to CSE IT Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Discuss about the limitations of Operation Research.
In the production of 2 types of toys, a factory uses 3 machines B and C. The time required to
produce the first type of toy is 6 hours, 8 hours and 12 hours in machines B and C respectively.
The time required to make the second type of toy is 8 hours, 4 hours and 4 hours in machines
B and C respectively. The maximum available time (in hours) for the machines C are
380, 300 and 404 respectively. The profit on the first type of toy is 5 dollars while that on the
second type of toy is 3 dollars. To find the number of toys of each type that should be produced
to get maximum profit, formulate the problem as an LPP and solve it.
2. Use simplex method to find an improved solution for the linear problem represented by the
following tableau shown in Table 1 where basic variables are s1, s2, s3.
Table 1
x1 x2 s1 s2 s3 b Basic Variables
1 1 0 0 11 s1
1 1 0 1 1 27 s2
2 5 0 0 1 90 s3
0 0 0 0
The objective function for this problem is 4x1 6x2.
Solve the following problem by two phase simplex method
max z=2x1+3x2+x3
x1+ x2+x3 40
2x1+ x2-x3 10
x2+x3 10
x1, x2, x3 0
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UNIT II
3. Explain Vogel's approximation method to find initial basic feasible solution of a given transportation
problem with an example.
A contractor pays his subcontractors a fixed fee plus mileage for work performed. On a given day
the contractor is faced with three electrical jobs associated with various projects. Given Table 2
are the distances between the subcontractors and the projects.
Table 2
A B C
Westside 50 36 16
Federated 28 30 18
Goliath 35 32 20
Universal 25 25 22
How should the contractors be assigned to minimize total costs?
4. How to achieve optimal solution in Hungarian assignment method?
Solve the assignment problem represented by the matrix shown in Table 3.
Table 3
Person 1 2 3 4
A 20 25 22 28
B 15 18 23 17
C 19 17 21 24
D 25 23 24 24
UNIT III
5. Explain Pure strategy Mixed strategy Value of the game and Fair game
There are four jobs each of which has to go through the machines Mi, in the order
M1,M2,…,M6. Processing times are given Table 4.
Table 4
Jobs(j) M1 M2 M3 M4 M5 M6
J1 20 10 9 4 12 27
J2 19 8 11 8 10 21
J3 13 7 10 7 9 17
J4 22 6 5 6 10 14
Determine a sequence for these four jobs which minimizes the total elapsed time, also find the
total elapsed time.
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6. Solve the gaming problem by graphical method.
Solve the 2x2 game with no saddle point.
UNIT IV
7. Explain the basic concepts of dynamic programming.
Solving Linear Programming using Dynamic Programming.
Maximize Z 3x1 5x2
Subject to x1 x2 3x1 2x2 18; x1; x2
8. Outline the significance of principle of optimality in dynamic programming with an example.

Find shortest route from node 1 to all other nodes by dynamic programming for Figure 1.
Figure 1
UNIT V
9. Illustrate the advantages of constrained programming.
Derive the Lagrangian function used in quadratic approximation.
10. Explain variable metrics method for constrained optimization.
Derive the mathematical form of direct quadratic optimization.