M.Sc. (Statistics) (Semester IV) (CGPA) Examination, 2017
OPERATIONS RESEARCH
Iiof
Day Date: Saturday, 29-04-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
N.B. Q. no. 1 and 2 are compulsory.
Attempt any three questions from Q. no. 3 to Q. no.7.
Attempt five questions.
Figures to the right indicate full marks.
Q.1 Select correct alternatives of the following questions. 05
1g) Which of the following is not assumption of an LPP?
Additivity Uncertainty
Proportionality Divisibility
If primal problem has unbounded feasible solution then
corresponding dual has
Unbounded feasible
solution
Optimum feasible solution
No feasible solution None of the above
In two person zero sum game is said to be fair if
The upper value and lower value of the game are not equal
The upper value is more than lower value of the game
The upper value and lower value of the game are same and
equal to zero.
None of the above
The solution of the linear programming problem is said to be
feasible if
Some of the xi's are positive
All xi's are non negative
The some xi's are zero and remaining are positive
None of these
The set of all convex combinations of finite number of points of
is set
Convex Concave Both a and b Neither a nor b
Fill in blanks. 05
Optimum basic feasible solution to the linear programming
problem corresponds point of feasible region.
If the players select the same strategy each time, then it referred
as
Quadratic programming problem is the particular case of
programming problem.
Simplex method is iterative method to solve programming
problem.
Page 2 of 2
Artificial variable technique used when
State whether true or false. 04
Quadratic programming problem have quadratic objective
function and linear constraints.
Mixed integer programming problem means all decision
variables must be integer.
Degenerate basic feasible solution means at least one basic
variable having value zero.
Degeneracy in an LPP may arise at the initial stage.
Q.2 What is mean by two person zero sum game? Define pure and
mixed strategies.
04
Show that if primal problem has optimum feasible solution then dual
also has optimum feasible solution.
04
What is integer linear programming problem? Define all and mixed
IIP with suitable examples.
03
Define the following terms,
Convex set
Supporting hyperplane
Separating hyperplane
03
Q.3 Describe dual simplex algorithm to solve linear programming
problem.
07
Use Dual Simplex Method to solve the following LPP.
Max
Subject to
And
07
Q.4 Write the simplex algorithm to solve linear programming problem. 07
Solve the following LPP using simple method.
Max
Subject to,
07
Q.5 What is linear programming problem? Write down general
mathematical linear programming problem and describe the terms
solution, feasible solution, optimum feasible solution.
07
Describe Branch and Bound method to solve integer linear
programming.
07
Q.6 Write a note on following.
Graphical method to solve mx2 or 2 or 2xn game.
Dominance and modified dominance property.
07



Solve the following game problem graphically.
07
Q.7 What is quadratic programming problem? Describe Wolfe's method
to solve QPP.
07
If x0 and y0 be the feasible solution to the primal
{maximize sub to Ax and corresponding
dual {minimize sub to y 0}.
Then show that Ax0 b'y0.