Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) M.Tech (ME is Master of Engineering) 2020 R19 EEE Optimization Techniques Model Previous Question Paper
I M. Tech I Semester (R19) Regular Examinations
OPTIMIZATION TECHNIQUES
Electrical & Electronic?s Engineering Department
MODEL QUESTION PAPER
TIME: 3Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT.
All questions carry equal marks.
*****
CO KL M
UNIT-I
1. a)
State an optimization problem. Give any five Engineering
applications of optimization.
1 K3 7M
b)
Find minimum value of the function f(X
1
, X
2
) = X
1
2
+ X
2
2
-
10 X
1
-10X
2
satisfying the constraints X
1
+X
2
? 9, X
1
-X
2
? 6
and X
1
, X
2
? 0 using Lagrangian multipliers.
1 K3 8M
OR
2. An advertising company has to plan their advertising
strategy thrgh the different media, namely TV, Radio
and Newspaper. The purpose of advertising is to reach
maximum number of potential customers. The cost of an
advertisement in TV, Radio and Newspaper are Rs
3000/-, Rs2000/- and Rs2500/- respectively. The
average expected potential customers reached per unit
by 20000 of which 15000 are female customers. These
figures with Radio are 60000 and 40000 and with
Newspaper 25000 and 12000 respectively. The
company has a maximum budget for advertising is
Rs50000/- only. It is proposed to advertise thrgh TV
or Radio between 6 and 10 units and atleast 5
advertisements shld appear in Newspaper. Further it
decides that atleast 100000 exposures shld take place
among female customers. Budget of advertising by
Newspaper is limited to Rs25000/- only. Formulate into
linear programming problem and solve it by using
simplex method.
1 K3 15M
UNIT-II
3. Minimize Z= X
1
-X
2
+2X
1
2
+ 2 X
1
X
2
+ X
2
2
with the
starting point (0,0) using the univariate method.
1 K3 15M
OR
4. Solve the following Linear Programming Problem by
Revised simplex method.
Maximize Z= 5X
1
+ 3X
2
Subject to 4X
1
+ 5X
2
? 10
5X
1
+ 2X
2
? 10 , 3X
1
+ 8X
2
? 12 And X
1
, X
2
? 0
1 K3 15M
UNIT-III
5. State Kuhn- Tucker conditions. Minimize f(X
1
, X
2
) =
(X
1
-1)
2
+ (X
2
-5)
2
,
Subject to -X
1
2
+ X2 ? 4
1 K4 15M
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[M19P1107]
I M. Tech I Semester (R19) Regular Examinations
OPTIMIZATION TECHNIQUES
Electrical & Electronic?s Engineering Department
MODEL QUESTION PAPER
TIME: 3Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT.
All questions carry equal marks.
*****
CO KL M
UNIT-I
1. a)
State an optimization problem. Give any five Engineering
applications of optimization.
1 K3 7M
b)
Find minimum value of the function f(X
1
, X
2
) = X
1
2
+ X
2
2
-
10 X
1
-10X
2
satisfying the constraints X
1
+X
2
? 9, X
1
-X
2
? 6
and X
1
, X
2
? 0 using Lagrangian multipliers.
1 K3 8M
OR
2. An advertising company has to plan their advertising
strategy thrgh the different media, namely TV, Radio
and Newspaper. The purpose of advertising is to reach
maximum number of potential customers. The cost of an
advertisement in TV, Radio and Newspaper are Rs
3000/-, Rs2000/- and Rs2500/- respectively. The
average expected potential customers reached per unit
by 20000 of which 15000 are female customers. These
figures with Radio are 60000 and 40000 and with
Newspaper 25000 and 12000 respectively. The
company has a maximum budget for advertising is
Rs50000/- only. It is proposed to advertise thrgh TV
or Radio between 6 and 10 units and atleast 5
advertisements shld appear in Newspaper. Further it
decides that atleast 100000 exposures shld take place
among female customers. Budget of advertising by
Newspaper is limited to Rs25000/- only. Formulate into
linear programming problem and solve it by using
simplex method.
1 K3 15M
UNIT-II
3. Minimize Z= X
1
-X
2
+2X
1
2
+ 2 X
1
X
2
+ X
2
2
with the
starting point (0,0) using the univariate method.
1 K3 15M
OR
4. Solve the following Linear Programming Problem by
Revised simplex method.
Maximize Z= 5X
1
+ 3X
2
Subject to 4X
1
+ 5X
2
? 10
5X
1
+ 2X
2
? 10 , 3X
1
+ 8X
2
? 12 And X
1
, X
2
? 0
1 K3 15M
UNIT-III
5. State Kuhn- Tucker conditions. Minimize f(X
1
, X
2
) =
(X
1
-1)
2
+ (X
2
-5)
2
,
Subject to -X
1
2
+ X2 ? 4
1 K4 15M
-(X
1
-2)
2
+ X
2
? 3 by Kuhn- Tucker conditions
OR
6.
Solve the following problem by Powell?s method (Use
pattern search directions) Minimize f(X
1
, X
2
) = 4X
1
2
+ 3X
2
2
-5 X
1
X
2
-8X
1
from starting point (0, 0).
1 K4 15M
UNIT-IV
7. Minimize f(X
1
,X
2
) = 6x
1
2
+ 3x
2
2
+4x
1
x
2
subject to
x
1
+x
2
-5 =0 solve the problem by using the interior
penalty function approach.
1 K3 15M
OR
8. Minimize f(X
1
,X
2
) = 1/3(x
1
+1)
3
+x
2
subject to g
1
(X
1
,X
2
)
1-x
1 ?
0, g
2
(X
1
,X
2
) = -x
2?
0. solve the problem by using
an exterior penalty function approach.
1 K2 15M
UNIT-V
9. Using Fibonacci method minimize Z= 12x - 3x
4
-2x
2
Take the initial interval as [0,2] and n=6. Calculate the
interval of uncertainty after 6 cycles.
1 K3 15M
OR
10. Find the minimum function f(x)=0.65-(0.75/(x
2
+1))-
(0.65x)tan
-1
(1/x) using the quadratic interpolation
method with an initial step size of 0.1. show calculations
for two refits.
1 K3 15M
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This post was last modified on 28 April 2020