M.Sc. (Semester IV) (CBCS) Examination Nov/Dec-2018
Statistics
OPTIMIZATION TECHNIQUES
Time: 2½ Hours Max. Marks: 70
Instructions: Attempt five questions.
Q. No. and Q. No. are compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Q.1 Select correct alternatives of the following questions: 05
The role of artificial variable in simplex method is
To obtain IBFS
To start phases of simplex method
To reduce objective function value
None of these
A constraint that does not affect the feasible region is a
Non-negativity constraint Redundant constraint
Standard constraint Slack constraint

5
0
Consider a linear programming problem
Maximize
Subject to the constraints,
Which of the following is not true?
One of the dual constraint is 10
The objective function of dual problem is Minimize
If and be the feasible solutions to primal and corresponding
dual problem, then
Dual variable corresponding to second constraint is unrestricted.
Which of the following is true regarding quadratic programming problem
Both objective function as well as constraints are quadratic in decision
variables
Objective function is linear but constraints are quadratic in decision
variables
Objective function is quadratic and constraints are linear in decision
variables
Both objective function and constraints are linear in decision variables
A two person game is said to be zero sum game if
Gain of one player is exactly equal to loss of other player
Gain of one player does not match the loss to other player
Both player must have same number of strategies
Diagonal entries of pay-off matrix are zero
Page 2 of 2
SLR-VR-492
Fill in the blanks: 05
Set of all feasible solutions is
In two-phase simplex method, objective function in phase 1 is
Dual of dual is
The linear programming problem with all decision variables can take only
two values zero and one called
A quadratic programming problem the is quadratic in decision
variables.
State whether the following statement are True or False. 04
A degenerate solution can never be optimum.
When additional variable is introduced in the LPP, the existing optimum
solution can further improved if − 0.
If linear programming problem have feasible then it also has basic
feasible solution.
In mixed integer programming problem, different objective functions are
mixed together.
Q.2 State and prove weak duality theorem. 03
Describe need of integer programming. 03
State advantage and disadvantages of graphical method for solving LPP. 04
State the characteristics of dynamic programming. 04
Q.3 Describe Two-Phase method of solving linear programming problem. 07
Use simplex method to solve. 07
−



0
Q.4 Describe Gomory's fractional cut method to solve mixed integer
programming problem.
07
Use branch and bound method to solve: 07


35,

0 and are integers
Q.5 Discuss relation between linear programming and dynamic programming.
Show how to solve a linear programming problem by dynamic programming
technique.
07
Describe Wolfe's method for solving QPP. 07
Q.6 Solve the following rectangular game problem graphically. 07
B1 B2 B3 B4
A1 2 1 0
A2 1 0 3 2
For two person zero sum game show that maximin value of the game is less
than or equal to the minimax value of the game.
07
Q.7 Obtain the range of change in objective function coefficient if it is
correspond to optimum basic variable.
07
State and prove fundamental theorem on duality.