ALCCS
NOTE:
· Question 1 is compulsory and
carries 28 marks. Answer any FOUR questions from the rest. Marks are indicated against each question.
· Parts of a question should be
answered at the same place.
· All
calculations should be up to three places of decimals.
Q.1 a. Discuss how revised simplex method can be used to improve
computational efficiency of solving a linear programming problem.
b. Discuss the economic
interpretation of the dual problem.
c. Differentiate
between unbounded solution and infeasible solution in the context of solution
to linear programming problem.
d. Explain
what is an unbalanced transportation problem.
e. Discuss
four applications of integer programming.
f. Discuss
degeneracy in linear programming problem?
g. Discuss the role of Operations Research in
decision making. (7
4)
Q.2 a. What
is the standard form of linear programming problem and how do you obtain it?
Also discuss special cases that arise in application of simplex method. (9)
b. Use penalty method to solve the following
linear programming problem: Maximize
z= 2x1+x2+x3
Subject
to
4x1+6x2+3x3<=8, 3x1-6x2-4x3<=1,
2x1+3x2-5x3>=4
and x1, x2,
x3<=0. (9)
Q.3 a. What are various algorithms for finding
initial basic solution for a transportation problem? Discuss them.
(9)
b. Determine the
basic feasible solution, if exists, to the following transportation
problem using Vogel’s Approximation method.
Distribution
Centres
Sources D1 D2 D3 D4 Supply
S1 2 3 11 7 6
S2 1 0 6 1 1
S3 5 8 15 9 10
Requirement 7 5 3 2
(9)
Q.4 a. What are various algorithms for solving an Integer Linear
programming problem? Discuss branch and bound method in detail. (9)
b. Using the cutting plane method, solve the
following Integer Linear Programming
Problem
Maximize z
= 7x1+10x2
Subject
to -x1+3x2<=6,
7x1+x2<=35, x1, x2 are
non-negative integers. (9)
Q.5 a. Discuss in detail the various parameters for
designing and evaluating a simulation
based experiments.
(9)
b. A student has to take examination in
three courses x, y, z. He has three days
available for study. He feels that it would be best to
devote a whole day to study the same course so that he may study
a course for one day, two days or three days or not at
all. His estimates of grades he may get by studying are as follows.
Study
days/courses x y z
0 1 2 1
1 2 2 2
2 2 4 4
3 4 5 4
How should the student plan to
study so that the grades obtained are maximized? (9)
Q.6 a. Discuss Hungarian Assignment algorithm in
detail.
(9)
b. A department has five employees with five
jobs to be performed. The time (in hrs) each man will take to perform each job
is given by the following cost matrix:
Employees
I II III IV V
Jobs A 10 5 13 15 16
B 3 9 18 13 6
C 10 7 2 2 2
D 7 11 9 7 12
E 7 9 10 4 12
How should jobs be allocated
one per employee so that total the man-hours can be maximized? (9)
Q.7 Write a short note on any THREE of the following:
(i) GPSS.
(ii) Degeneracy in Transportation Problem.
(iii)
Sensitivity and Parametric Analysis.
(iv)
Monte Carlo Method. (6+6+6)