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Posted Date: 08 Jan 2009 Posted By: gautham shenoy Member Level: Gold
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2005 Jawaharlal Nehru Technological University III B.Tech I Semester Supplementary Examinations, November 2005 OPTIMIZATION TECHNIQUES Question paper
Code No: NR310206 NR
III B.Tech I Semester Supplementary Examinations, November 2005
OPTIMIZATION TECHNIQUES
(Electrical & Electronic Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Explain with the help of examples, how optimization problems are classified
based on: [8]
i. Single value objective function
ii. Multi value objective function.
(b) Explain the formulation of any engineering problem. Include objective func-
tions and constraints. [8]
2. (a) State and explain the necessary and sufficient conditions for existence of rel-
ative optima in case of multivariable optimization with constraints. [8]
(b) Find the dimensions of a rectangular parallelepiped with largest volume whose
sides are parallel to the coordinate planes, to be inscribed in the ellipsoid. [8]
3. (a) State and explain the standard form of LPP. [8]
(b) Explain the significance of slack, surplus and artificial variables of LPP. [8]
4. (a) Explain the canonical form with respect to LPP. [6]
(b) Solve the following system of equations by using PIVOT operations
4x1 + 3x2 + x3 = 13
3x1 + 0x2 + 7x3 = 24
x1 + 2x2 + 3x3 = 14
[10]
5. (a) With the help of an example discuss unbalanced transportation problem [6]
(b) Solve the following transportation problem
Availability
30 20 10 800
5 15 25 500
Requirement 300 300 400 [10]
6. Starting from (0,0) , carry out at the most five iterations for the following problem
using the method of steepest descent : [16]
Minimize f(x) = (x1 - x2
2)2 + (1 - x2
2).
7. Classify the constrained optimization techniques and briefly explain each technique.
[16]
Code No: NR310206 NR
8. Explain the concept of dynamic programming and show how to solve a linear pro-
gramming problem by dynamic programming approach with an example. [16]
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