MCA (Science) (Semester (CBCS) Examination, 2017
OPEARTIONS RESEARCH
Day Date: Saturday, 22-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
N.B. Q.1 and Q.2 are compulsory.
Attempt any three questions from Q. no. 3 to Q. no. 7.
Figures to the right indicate full marks.
Q.1 Choose the correct alternatives. 10
Operation Research attempts to find the best
to a problem.
Optimum Perfect Degenerate None of above
The objective function constraints are linear relationship
between
Variables Constraints Function All of above
Graphic method can be applied to solve a LPP when there are
only ____variable.
One More than one Two Zero
If the feasible region of a LPP is empty, the solution is
Infeasible Unbounded
Alternative None of these
In simplex method we add variables in the case of
Slack variable Surplus variable
Artificial variable None of these
another method to solve a given LPP involving some
artificial variable?
Big-M method Method of Penalties
Two-phase simplex method None of these
A feasible solution to a transportation problem containing m
origins n destination is said to be
Independent Degenerate
Both A B Non degenerate
One can find the initial basic feasible solution by using
VAM MODI Optimality test None of these
A s-t cut is a partition of the vertices
S A t B t A S B
Page 2 of 3
S A t A t A t B
10) If the total supply is less than the total demand, a dummy source
is included in the cost matrix with
Dummy demand Dummy supply
Zero cost Both A B
Fill in the blanks. 04
is a simple s t path P in the residual graph G.
An extreme point is the point of the set.
Critical event is defined as the difference between
event time.
The long form of Project management PERT is
Q.2 Define Feasible solution 04
Basic feasible solution
Explain convex function with example. 03
Write the Advantages of Linear programming Techniques. 03
A hyperplane in Rn is a convex set. 04
Q.3 Explain the graphical method of a solving a linear programming
problem involving two variables.
07
Use Two-phase simplex method to the solve following LPP.
Maximize
Subject to the constraints
07
Q.4 Solve the following problem by dual simplex method
Maximize
subject to the constraints

07
Explain the Kuhn-Tucker condition. 07
Q.5 Find the Initial Basic solution of the following Transportation
problem
08
Warehouse
factory
W1 W2 W3 W4 Factory
capacity
F1 19 30 50 10 7
F2 70 30 40 60 9
F3 40 8 70 20 18
Warehouse
requirement
5 8 7 14 34
If X is any feasible solution to the primal W is any feasible
solution to the dual problem by simplex method then
06
Q.6 Explain the Max-flow Min-cut Theorem. 07
Explain the Matroid with example. 07
Q.7 Determine the critical path calculate the slack time for each event
for the following PERT.
Diagram
08
Explain the ford-fulkerson algorithm.