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Previous Year Exam Questions of Optimization in Engineering of BPUT - OE by Verified Writer

  • Optimization in Engineering - OE
  • 2017
  • PYQ
  • Biju Patnaik University of Technology Rourkela Odisha - BPUT
  • Electrical and Electronics Engineering
  • B.Tech
  • 24706 Views
  • 336 Offline Downloads
  • Uploaded 1 year ago
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Registration No: Total Number of Pages: 03 B.Tech HSSM 3302 5th Semester Back Examination 2017-18 Optimization in Engineering BRANCHE : AEIE, CHEM, CSE, ECE, EEE, EIE, ELECTRICAL, ENV, ETC, FASHION, FAT, IT, ITE, MANUFAC, MANUTECH, MARINE, METTA, MINERAL, MINING, MME, PLASTIC, TEXTILE Time: 3 Hours Max Marks: 70 Q.CODE: B159 Answer Question No.1 which is compulsory and any five from the rest. The figures in the right hand margin indicate marks. Q1 a) Answer the following questions : Express the LPP in standard form Maximize Z= 7 x1  4 x 2 Subject to 3x1  x2  5 2x1  x2  4 x1 , x2  0 b) Define a degenerate basic feasible solution. c) Obtain the dual of the following problem Maximize Z=  3x1  5 x 2 Subject to x1  3x2  2x3  6 2x1  x2  5x2  7 x1 , x2 , x3  0 d) What is an integer programming problem? e) Why transportation Problem is also a linear programming problem? f) What do you mean by degeneracy in a transportation problem? g) What are the basic characteristics of a queueing system? h) What is Bordered Hessian matrix? i) What is the advantage of Golden search method over Fibonacci search method? Define local maximum and global maximum of a function. j) (2 x 10)

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Q2 a) (5) Solve the following LPP by graphical method Minimize Z= 5 x1  3 x 2 Subject to 2x1  x2  6 3x1  x2  4 x1, x2  0 b) (5) Solve by Simplex method Minimize Z= 4 x1  x 2 Subject to 3x1  4x2  20 x1  5x2  15 x1 , x2  0 Q3 Use revised simplex method to solve the following LPP (10) Maximize Z= 3 x1  2 x 2 Subject to x1  2x2  4 3x1  2x2  6 x1  4x2  2 x1 , x2 , x3  0 Q4 Find the optimum integer solution of the following integer programming problem (10) Minimize Z= 2 x1  3x 2 Subject to 6x1  3x2  20 x1  4x2  10 x1 , x2  0 Q5 a) are integers. Solve the transportation problem to maximize the profit Source A B C Demand P 40 44 38 40 Destination R S 22 33 30 30 28 30 60 30 Q 25 35 38 20 (5) Supply 10 30 70 (5) b) Solve the assignment problem Job / Person P Q R S A B C D 10 12 33 17 20 35 20 23 25 15 12 26 20 10 26 25

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Q6 Solve the following problem by using the method of Lagrangian multiplier 2 2 Minimize Z= x1  x 2  x3 (10) 2 Subject to 2 4x1  x2  2x3 14  0 x1 , x2 , x3  0 Q7 (10) Solve the quadratic programming problem 2 Maximize Z= 4 x1  6 x 2  2 x1  2 x1 x 2  2 x 2 2 Subject to x1  2x2  2x3  2 x1 , x2  0 Q8 a) Use Golden search method to minimize the function 4 3 (5) 2 f ( x)  x  15 x  72 x  1135x Terminate the search when | f ( x n )  f ( x n 1 )  0.5 where the initial range of x is 1  x  15 b) Write short notes on genetic algorithm. (5)

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