Biju Patnaik University of Technology 2010 B.Tech Information Technology /OPTIMIZATION IN ENGINEERING - Question Paper

1.Answer the subsequent question:

(a) describe a linear programing issue in standard form.
(b) describe basic feasible solution and optimal solution of linear programming issue.
(c) Write an application of linear programming.
(d) discuss Stepping Stone method of transportation issue.
(e) elaborate the advantages of MODI method of transportation issue.
(f) discuss primal programme and dual programme.
(g) What is sensitive analysis ?
(h) Write an application of integer programming.
(i) What is Fibonacci search?
(j) State Kuhn-Tucker conditions in non-linear programming.

2. A manufacturer of wooden articles produces tables and chairs which require 2 kinds of inputs namely ,they being wood and labour. The manufacturer knows that for a table three units of wood and one
unit of labour are needed while for a chair they are two units every.The profit from every table is Rs.20 while it is Rs.16 for every 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 issue as linear programming issue.

3.Solve the subsequent 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 subsequent linear programming problem:
Maximize z=x1+2x2
Subject to:
-x1+2x2<=8,
x1+2x2<=12,
x1-2x2<=3,
x1>=0 and x2>=0

4. Solve the subsequent integer programming issue 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. find the set of necessary conditions for the non-linear 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. obtain the dimension of rectangular parallelopiped with largest quantity 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 Kuhn-Tucker conditions for the issue :
Minimize z=2x1 + 3x2 - x1^2 -2x2^2
Subject to the conditions:
x1 + 3x2 <=6,
5x1 + 2x2 <=10,
x1,x2>=0

Earning:   Approval pending.