Download JNTUK M-Tech 2020 R19 IT Optimization Techniques Model Question Paper

Download JNTUK (Jawaharlal Nehru Technological University Kakinada (JNTU kakinada)) M.Tech (ME is Master of Engineering) 2020 R19 IT Optimization Techniques Model Previous Question Paper

7

[M19 IT 1106]

I M. Tech I Semester (R19) Regular Examinations
OPTIMIZATION TECHNIQUES
Department of Information Technology
MODEL QUESTION PAPER
TIME: 3 Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****
CO KL M
UNIT - I
1. a). Classify and explain varis types of optimization problems with
examples.
1 4 8
b). Identify the necessary & sufficient conditions for multivariable
optimization problem witht constraints.
1 3 7
OR
2. a). solve the maximum or minimum of the function f(x)=x
1
2
+x
2
2
+x
3
2
-4x
1
-8x-
12x
3
+56
1 4 8
b). Distinguish the gradient of the function and its importance in optimization. 1 4 7

UNIT - II
3. a). Identify transportation problem and represent it mathematically. 2 3 7
b). Min f(x) =x
1
2
-x
1
x
2
+3x
2
2
. Starting point (1,2) by using steepest descent
method. Solve calculations for two cycles.
1 4 8
OR
4. a). Solve the following non-LPP by Lagrangian multiplier method: Min Z=
4x
1
2
+ 2x
2
2
+ x
3

- 4x
1
x
2;
st x
1
+ x
2
+ x
3
=15, 2x
1
- x
2
+2x
3
= 20 and x
i
?0 ? i
2 4 7
b). Identify the Kuhn-Tucker conditions min cost flow problem 2 3 8
UNIT - III
5. a). Compare single server and multiple server models 2 4 8
b). List t Probabilistic inventory control models 2 4 7
OR
6. a). Classify the terminologies involved in dynamic programming. 2 4 8
b).
Identify the importance of gradient methods.
2 3 7
UNIT - IV
7. a). Classify the characteristics of a constrained non-linear programming
problem.
3 4 8
b).
Identify the suitable examples for design constraints and objective
function
3 3 7
OR
8. a).
Analyze Greedy algorithm with example
3 4 7
b). Prove that a graph of n vertices is a complete graph if its chromatic
polynomials P
n
(?) = ? (? ? 1) (? ? 2) ? (? - n + 1)
4 5 8
UNIT - V
9.
a). Identify necessary and sufficient conditions of non-LPP with single
3 3 7
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7

[M19 IT 1106]

I M. Tech I Semester (R19) Regular Examinations
OPTIMIZATION TECHNIQUES
Department of Information Technology
MODEL QUESTION PAPER
TIME: 3 Hrs. Max. Marks: 75 M
Answer ONE Question from EACH UNIT
All questions carry equal marks
*****
CO KL M
UNIT - I
1. a). Classify and explain varis types of optimization problems with
examples.
1 4 8
b). Identify the necessary & sufficient conditions for multivariable
optimization problem witht constraints.
1 3 7
OR
2. a). solve the maximum or minimum of the function f(x)=x
1
2
+x
2
2
+x
3
2
-4x
1
-8x-
12x
3
+56
1 4 8
b). Distinguish the gradient of the function and its importance in optimization. 1 4 7

UNIT - II
3. a). Identify transportation problem and represent it mathematically. 2 3 7
b). Min f(x) =x
1
2
-x
1
x
2
+3x
2
2
. Starting point (1,2) by using steepest descent
method. Solve calculations for two cycles.
1 4 8
OR
4. a). Solve the following non-LPP by Lagrangian multiplier method: Min Z=
4x
1
2
+ 2x
2
2
+ x
3

- 4x
1
x
2;
st x
1
+ x
2
+ x
3
=15, 2x
1
- x
2
+2x
3
= 20 and x
i
?0 ? i
2 4 7
b). Identify the Kuhn-Tucker conditions min cost flow problem 2 3 8
UNIT - III
5. a). Compare single server and multiple server models 2 4 8
b). List t Probabilistic inventory control models 2 4 7
OR
6. a). Classify the terminologies involved in dynamic programming. 2 4 8
b).
Identify the importance of gradient methods.
2 3 7
UNIT - IV
7. a). Classify the characteristics of a constrained non-linear programming
problem.
3 4 8
b).
Identify the suitable examples for design constraints and objective
function
3 3 7
OR
8. a).
Analyze Greedy algorithm with example
3 4 7
b). Prove that a graph of n vertices is a complete graph if its chromatic
polynomials P
n
(?) = ? (? ? 1) (? ? 2) ? (? - n + 1)
4 5 8
UNIT - V
9.
a). Identify necessary and sufficient conditions of non-LPP with single
3 3 7
8

equality constraint.
b).
A company produces two types of hats. Each hat of first type requires
twice as much as labr time as second type. If all hats are of the
second type only, the company can produce a total of 500 hats a day.
The market limits daily sales of the first and second type to 150 and
250 hats. Assuming that the profits per hat are Rs.8 for type A and Rs.5
for type B, In the stated problem solve:
a) Design Vector b) Objective Function
3 4 8

OR

10. a).
Classify balanced transportation problem.
4 4 8
b).
List t varis methods for finding an initial basic feasible solution
for a transportation problem.
4 4 7





































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