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[M19P1107]
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I M. Tech I Semester (R19) Regular Examinations
OPTIMIZATION TECHNIQUES
Electrical & Electronic’s Engineering Department
MODEL QUESTION PAPER
TIME: 3Hrs. Max. Marks: 75M
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Answer ONE Question from EACH UNIT.
All questions carry equal marks.
CO | KL | M
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UNIT-I
- a) | State an optimization problem. Give any five Engineering 1 K3 M applications of optimization.
b) | Find minimum value of the function f(X1, X2) = X1² + X2 - 1 K3 M 10X1-10X2 satisfying the constraints X1+X2 = 9, X1-X2 = 6 and X1, X2 = 0 using Lagrangian multipliers.
OR
- An advertising company has to plan their advertising 1 K3 M strategy through 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 through TV or Radio between 6 and 10 units and at least 5 advertisements should appear in Newspaper. Further it decides that at least 100000 exposures should 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:
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UNIT-II
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- Minimize Z= X1-X2+2X1² + 2 X1X2+ X2² with the 1 K3 [15M starting point (0,0) using the univariate method.
OR
- Solve the following Linear Programming Problem by 1 K3 M Revised simplex method.
Maximize Z= 5X1+ 3X2 Subject to 4X1+ 5X2 = 10 5X1+ 2X2 = 10 5 3X1+ 8X2 = 12 And X1, X2 = 0
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UNIT-III
- State Kuhn- Tucker conditions. Minimize f(X1, X2) = 1 K4 M (X1-1)² + (X2-5)², Subject to -X1² + X2 = 4
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(X2 +X1=3 by Kuhn- Tucker conditions
OR
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- Solve the following problem by Powell’s method (Use 1 K4 M pattern search directions) Minimize (X1, X2) = 4X1² + 3X2² -5 X1X2-8X from starting point (0, 0).
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UNIT-IV
- Minimize f(X1,X2) = 6x1² + 3x2² +4x1x2 subject to 1 K3 15M X1+X2-5 =0 solve the problem by using the interior penalty function approach.
OR
- Minimize f(X1,X2) = 1/3(x1 +1)²+x2 subject to g1(X1,X2) 1 K2 15M 1-x1 =0, g2(X1,X2) = -X2= 0. solve the problem by using an exterior penalty function approach.
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UNIT-V
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- Using Fibonacci method minimize Z= 12x - 3x²-2x³ 1 K3 M Take the initial interval as [0,2] and n=6. Calculate the interval of uncertainty after 6 cycles.
OR
- Find the minimum function f(x)=0.65-(0.75/(x’+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.
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This download link is referred from the post: JNTUK M.Tech R19 2020 Model Question Papers || JNTU kakinada (All Branches)
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