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Code No: OR210253

II B.Tech I Semester Supplementary Examinations, May 2005 OPTIMIZATION TECHNIQUES (Electrical & Electronic Engineering) Time: 3 hours Max Marks: 70 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Explain the theory of multivariable optimization without constraints. (b) What is objective function? Explain the objective function surfaces. 2. (a) Explain single variable optimization with illustrative example. (b) Find the extreme points of the function. f (x1 , x2 ) = x31 + x32 + 2x21 + 2x22 + 6. 3. Solve the following system of equations by using pivot operations. 4x1 +3x2 +x3 = 13 3x1 +7x3 = 24 x1 +2x2 +3x3 = 14 4. (a) Give a generalized mathematical model of Linear Programming Problem. (b) Explain about the Basic Feasible Solution. (c) Explain the significance of ’key row’, ’key column’ and ’key number’ and ’replacement ratio’ with respect to a Simplex Method. 5. Maximize the following problem using Simplex Method. Z = 10x + y + 2z Subject to x + y − 2z ≤ 10; 4x + y + z ≤ 20 and x, y and z 0 6. An oil company has three refinery stations and five filling stations. Transportation cost (rupees for barrel) for shipping oil from refinery station to filling station is shown in the following table. Filling Station Capacities F1 F2 F3 F4 F5 (barrels) Refinery R1 360 180 270 180 540 24 Station R2 450 360 450 180 90 36 R 3 540 450 360 630 270 42 Requirementes

12 12 18 24 24

7. Solve the following problem using dynamic programming technique: Maximized z = 28x + 7y Subject to: 4x + 3y ≤ 12; 2x1 +5x2 ≤ 10; x1 , x2 ≥ 0. 8. Write short notes on the following: (a) Kuhn-Rucker conditions 1 of 2

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Code No: OR210253 (b) Limitations of Dynamic Programming Technique (c) Simplex algorithm. ?????

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OR210253 II B.Tech I Semester Supplementary Examinations, May ...

Maximize the following problem using Simplex Method. Z = 10x + y + ... 10; x1, x2 ≥ 0. 8. Write short notes on the following: (a) Kuhn-Rucker conditions. 1 of 2 ...

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