B.C.A (Semester III) (CBCS) Examination Oct/Nov-2017
OPERATIONS RESEARCH
Day Date: Saturday, 18-11-2017 Max. Marks: 70
Time: 02.30 PM to 05.00 PM
Instructions: All questions are compulsory.
Figures to the right indicate full marks.
Use of calculator is allowed.
Q.1 Choose the correct alternative. 14
To find the optimal solution, we
LPP VAM
MODI Method Rim
method is used to solve an assignment problem.
Elurian Hamiltion
Hungarian None of these
A given TP is said to be unbalanced, if the total supply is not equal to the

Optimization Demand
Cost None of these
The dual of LPP is
Dual Primal
Standard None of these
The objective of TP is to the total transportation cost.
Maximize Optimize
Minimize Stabilize
The graphical method of solving LPP can be used when the numbers of
variables in the objective function
0 1
3 2
Hungarian method is the method of
Assignment problem Transportation problem
Linear programming problem Dual problem
Optimal solution is a feasible solution (not necessarily basic) which minimizes

Time taken Partial cost
Total cost None of the above
If demand is lesser than supply then dummy demand node is added to make it
a
Simple problem Balanced problem
Transportation problem None of the above
10) The collection of all feasible solution is known
Total feasible solution Combined solution
Feasible region None of these
11) Standard form of LPP has the characteristics of
All constants are equations except for the non-negativity condition.
The right hand side element of each constant equation is non negative.
All variables are non-negatives.
All of above.
12) The non-negative variable that has to be added to a constraints inequality of
the form to change it to an equation is
Slack variable Surplus variable
Artificial slack variable None of these
13) If one or more values of the basic variables are zero valued then the solution
of the system is said to
Non degenerate solution Degenerate solution
Inconsistent solution None of the these
14) Any set of non-negative allocations which satisfies the raw and column
sum (rim requirement) is called a
Linear programming Basic feasible solution
Feasible solution None of the above
Q.2 Answers to the following. [Any seven] 14
Convert the following A.P of maximization type in to minimization type.
Define decision variable.
Write standard form of following LPP.
Maximize z=25x+36y subject to
Define balanced T.P.
Define surplus variable.
Give the steps to formulate LPP.
Define non degenerate solution of T.P.
Give the method of finding IBFS in T.P.
Define objective function with example.
Q.3 Attempt any two of the following. 10
A company produces T.V and Washing Machine. The weekly production
cannot exceed 20 T.V's and 30 Washing Machines. There are 60
workers.
A T.V requires 2 men weeks and a Washing Machine requires 1 man
week of labour. A T.V gives a profit of Rs. 1600 and a Washing Machine
gives a profit Rs. 1000. Find weekly production of each so as to maximize
the profit.
Write the dual of the following LPP.
Maximize 5x1+12x2+4x2.
Subject to x1+2x2+4x3≤10.
2x1-x2+3x3≤8.
x1, x2, x3≥0.
A marketing manager has 5 salesmen and 5 sales district. Considering of
the salesmen and the nature of district, the marketing manger estimates
that sales per month (in hundred rupees) for each salesman in each
district would be as follows.
Salesman
District
A B C D E
1 32 38 40 28 40
2 40 24 28 21 36
3 41 27 33 30 37
4 22 38 40 35 39
5 29 33 40 35 39
Find the assignment of salesmen to districts that will result in a maximum
sale.
Define canonical form of LPP. Give any example. 04
Q.4 Answer the following (Any 14
Maximize z=4x+5y subject to
3x+2y≤60, 3x+10y≤182.
y≥0.
Obtain initial basic feasible solution for the following problem by Northwest
corner method.
Warehouse
P Q R S
A 6 5 8 5 30
Factory B 5 11 9 7 40
C 8 9 7 13 50
35 28 32 25 120
Find solution of Transportation Problem using Least Cost method.
TOTAL no. of supply constraints: 3
TOTAL no. of demand constraints: 4
Problem Table is
D1 D2 D3 D4 Supply
S1 11 13 17 14 250
S2 16 18 14 10 300
S3 21 24 13 10 400
Demand 200 225 275 250
Q.5 Answer the following (Any 14
Find IBFS by VAM and optimal solution by MODI.
I II III IV ai
A 15 10 17 18 2
B 16 13 12 13 6
C 12 17 20 11 7
Bj 3 3 4 5 15
Write the dual, solve it and hence obtain the solution of primal.
Minimize z=2x1+2x2
Subject to 2x1+4x2≥1.
X1+2x2≥1.
2x2+x2≥1.
X1, x2x2≥0.
Write the following assignment problem for minimum cost by Hungarian
method.