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Posted Date: 08 Jan 2011 Posted By:: Abhishek Samrat Member Level: Silver Points: 5 (₹ 1)

2010 Biju Patnaik University of Technology B.Tech. Information Technology B.Tech/OPTIMIZATION IN ENGINEERING Question paper
1.Answer the following question:
(a) Define a linear programing problem in standard form. (b) Define basic feasible solution and optimal solution of linear programming problem. (c) Write an application of linear programming. (d) Explain Stepping Stone method of transportation problem. (e) What are the advantages of MODI method of transportation problem. (f) Explain primal programme and dual programme. (g) What is sensitive analysis ? (h) Write an application of integer programming. (i) What is Fibonacci search? (j) State KuhnTucker conditions in nonlinear programming.
2. A manufacturer of wooden articles produces tables and chairs which require two types of inputs namely ,they being wood and labour. The manufacturer knows that for a table 3 units of wood and 1 unit of labour are required while for a chair they are 2 units each.The profit from each table is Rs.20 while it is Rs.16 for each chair.The total available resources for the manufacturer are 150 units wood and 75 units of labour.The manufacturer wants to maximize his profit by distributing his resources for tables and chairs.Formulate the problem as linear programming problem.
3.Solve the following linear programming graphically: Minimize z=2x1+x2 Subject to x1 + x2 >=1, x1 + 2x2 <=10,x2<=4 and x1>=0,x2>=0.5.
3.Use simplex method to solve following linear programming problem: Maximize z=x1+2x2 Subject to: x1+2x2<=8, x1+2x2<=12, x12x2<=3, x1>=0 and x2>=0
4. Solve the following integer programming problem using branch and bound method : Maximize z=6x1+8x2 Subject to the conditions 4x1+16x2<=32 14x1+4x2<=28, x1,x2>=0 and are integers.
5. Obtain the set of necessary conditions for the nonlinear programming problem: Maximize z=x1^2+3x2^2 +5x3^2 Subject to the constraints: x1+x2+3x3=2, 5x1+2x2+x3=5, and x1,x2,x3 >=0.
6. Find the dimension of rectangular parallelopiped with largest volume whose sides are parallel to the coordinate planes,to be inscribed in the ellipsoid g(x,y,z)=x^2/a^2 + y^2/b^2 + z^2/c^2 1=0.
7. Derive the optimal solution from the KuhnTucker conditions for the problem : Minimize z=2x1 + 3x2  x1^2 2x2^2 Subject to the conditions: x1 + 3x2 <=6, 5x1 + 2x2 <=10, x1,x2>=0
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