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- 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

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)

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

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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