Operations Research
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Code: 9A05603
III B. Tech II Semester (R09) Regular Examinations, April/May 2012
OPTIMIZING TECHNIQUES
(Common to Computer Science & Engineering & Computer Science & Systems Engineering)
Time: 3 hours
Max Marks: 70
1
(a)
(b)
2
Answer any FIVE questions
All questions carry equal marks
*****
State the necessary and sufficiency conditions for the minimum of the single variable function f ( x ) .
Find the minimum of the function: f ( x ) = 10 x 6 − 48 x 5 + 15 x 4 + 200 x 3 − 120 x 2 − 480 x + 100 .
0.0
using
0.0
2
2
Minimize f ( x1 , x 2 ) = x1 − x 2 + 2 x1 + 2 x1 x 2 + x 2 starting from the point X1 =
D
L
Hooke and Jeeves’ method. Take ∆x1 = ∆x 2 = 0.8 and ε = 0.1.
3
A firm produces three products. These products are processed on three different machines. The time required to manufacture one unit of each of three products and the daily capacity of the three machines are given in the table below:
Machine
M1
M2
M3
R
O
Time per unit
(minutes)
2
3
2
4
-3
2
5
--
T
N
W
U
Machine capacity
(minutes / day)
440
470
430
The profit for product 1, 2, and 3 is Rs. 4, Rs. 3 and Rs. 6 respectively. It is assumes that all the amounts produced are consumed in the market. Formulate the problem as LPP in order to determine the daily number of units to be manufactured for each product.
J
4
Describe the transportation problem. Formulate the transportation problem as a linear programming problem.
5
Using Lagrange multiplier method solve following problem:
Minimize f (X) = 1/2(x12 + x22 + x32). subject to constraints: g1(x) = x1 − x2 = 0. g2(x) = x1 + x2 + x3 − 1 = 0.
6
(a)
(b)
Explain method of multipliers algorithm.
Describe briefly differences between the MOM and other transformation methods such as SUMT.
Contd. in Page 2
www.jntuworld.com
www.jntuworld.com
www.jwjobs.net
1
Code: 9A05603
Page 2
7
www.jwjobs.net
1
Code: 9A05603
III B. Tech II Semester (R09) Regular Examinations, April/May 2012
OPTIMIZING TECHNIQUES
(Common to Computer Science & Engineering & Computer Science & Systems Engineering)
Time: 3 hours
Max Marks: 70
1
(a)
(b)
2
Answer any FIVE questions
All questions carry equal marks
*****
State the necessary and sufficiency conditions for the minimum of the single variable function f ( x ) .
Find the minimum of the function: f ( x ) = 10 x 6 − 48 x 5 + 15 x 4 + 200 x 3 − 120 x 2 − 480 x + 100 .
0.0
using
0.0
2
2
Minimize f ( x1 , x 2 ) = x1 − x 2 + 2 x1 + 2 x1 x 2 + x 2 starting from the point X1 =
D
L
Hooke and Jeeves’ method. Take ∆x1 = ∆x 2 = 0.8 and ε = 0.1.
3
A firm produces three products. These products are processed on three different machines. The time required to manufacture one unit of each of three products and the daily capacity of the three machines are given in the table below:
Machine
M1
M2
M3
R
O
Time per unit
(minutes)
2
3
2
4
-3
2
5
--
T
N
W
U
Machine capacity
(minutes / day)
440
470
430
The profit for product 1, 2, and 3 is Rs. 4, Rs. 3 and Rs. 6 respectively. It is assumes that all the amounts produced are consumed in the market. Formulate the problem as LPP in order to determine the daily number of units to be manufactured for each product.
J
4
Describe the transportation problem. Formulate the transportation problem as a linear programming problem.
5
Using Lagrange multiplier method solve following problem:
Minimize f (X) = 1/2(x12 + x22 + x32). subject to constraints: g1(x) = x1 − x2 = 0. g2(x) = x1 + x2 + x3 − 1 = 0.
6
(a)
(b)
Explain method of multipliers algorithm.
Describe briefly differences between the MOM and other transformation methods such as SUMT.
Contd. in Page 2
www.jntuworld.com
www.jntuworld.com
www.jwjobs.net
1
Code: 9A05603
Page 2
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