Name
Reg No
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
07 THRISSUR CLUSTER
SECOND SEMESTER M.TECH. DEGREE EXAMINATION APR 2017
Mechanical Engineering Department
Production Engineering
07ME6242 OPTIMIZATION TECHNIQUES FOR
MANUFACTURING PROCESS
Time:3 hours Max.marks: 60
Answer all six questions. Part of each question is compulsory.
Answer either part or part of each question
Q.no. Module 1 Marks
1a Explain the term artificial variables and its use in linear programming 4
Answer b or c
b Using Simplex Method Maximize Z 3x1 2x2 5x3 subject to the
following constraints
x1 2x2 x3 430
3x1 2x3 460
x1 4x3 420
and x1, x2, x3 1 0
5
c Use the two phase method to solve the following LP problem
Maximize Z 3x1 x2 subject to
2x1 x2 1 2
x1 3x2 2
x2 4
and x1, x2 1 0
5
Q.no. Module 2 Marks
2a Explain what is meant by Kuhn-Tucker necessary conditions. 4
Answer b or c
b Using the method of Lagrangian multipliers minimise Z 3x1
2 x2
2 x3
2
Subject to x1 x2+x3 2 and x1, x2,x3 1 0
5
c Discuss the economic interpretation of Lagrangian multipliers and the
duality theory.
5
Q.no. Module 3 Marks
3a Explain the terms Local optimum point, Global optimal point and
Inflection point.
4
Answer b or c
b Minimize the function x2 in the interval 0 x 1 5. Take the
number of intermediate points n 4.
5
c Minimise f 2 x1
2 x2
2 by using the steepest descent method with the
starting point (two iterations only).
5
Q.no. Module 4 Marks
4a State some problem areas in management where goal programming might
be applicable.
4
Answer b or c
b 5
c Discuss the weighting method of solution for solving multi objective
optimisation problem.
5
Q.no
.
Module 5 Mark
s
5a Explain Stochastic process with suitable examples. 5
Answer b or c
b A company reviews the state of its important annually and decides whether
it is successful or unsuccessful. The company must decide whether or not to
advertise the products to further promote sales. The following matrices P1
and P2 provide the transition probabilities with and without advertisement
during any year. The associated returns are given by matrices R1 and R2.
Find the optimal decisions over the next 3 years.
7
c A company can advertise through radio, TV or newspaper. The weekly
costs of advertisement on the three media are estimated at Rs 200, Rs 900
and Rs 300 respectively. The company can classify its sales volume during
each week as fair, good or excellent. A summary of the transition
probabilities associated with each advertisement medium follows.
Find the optimal advertisement policy over the next 3 weeks.
7
Q.no. Module 6 Marks
6a What is an NP hard problem? Give examples. 5
Answer b or c
b Use genetic algorithm to find minimum of following function
y 0-x
Perform for 2 iterations. Use the given random number table-1.
7
c Use simulated annealing to solve the following function
0.2 x2 +450/x 0.5-x -25.5
Perform for 4 iterations. Use the given random number table-1.
Table-1. Random number table
Sl
No:
Random
number
Sl
No:
Random
number
Sl
No:
Random
number
Sl
No:
Random
number
1 0.993952 6 0.76637 11 0.422163778 16 0.312892
2 0.850928 7 0.646286 12 0.631429118 17 0.669927
3 0.664032 8 0.345723 13 0.526440039 18 0.182741
4 0.967061 9 0.586837 14 0.397067073 19 0.499687
5 0.32409 10 0.21327 15 0.961783885 20 0.526077
7