B.Com. III (Semester
VI) (CGPA) Examination, 2018
statistics (Paper II)
Advanced Statistics
Day and Date Saturday, 8-12-2018 Max. Marks 70
Time 2.30 p.m. to 5.00 p.m.
Instructions All questions are compulsory and carry equal marks.
Figures to the right indicate full marks.
1. Choose the most appropriate alternative amongst the given for each question. 14
To find the optimum solution we apply
L.P.P. V.A.M.
MODI method None of these
The graphical method of L.P.P. uses
Objective function equation Constraint equations
Linear equations All of the above
Assignment Problem (A.P.) is a particular case of
L.L.P. T.P.
Both and None of these
If the total requirement and total availability are not equal then T.P. is
Balanced Unbalanced
Degenerate None of these
To solve an assignment problem the method used is
Hungarian Hamilton
Elurian None of these
Any set of non negative allocations (Xij which satisfies the row and
column sums (rim requirements) is called as
Basic feasible solution Feasible solution
No solution None of these
Which of the following is a valid objective function for an L.P.P.
max. 5xy min. 4x 3y
max. 5x2 6y2 None of these
The maximisation or minimisation of a quantity is the
Constraint of the L.P.P
Objective of the L.P.P.
Goal of the management science
None of these
An A. P. with cost matrix of m rows and columns is said to be unbalanced if
m n m n
m n Both and
10) An unbalanced A. P. with m rows n columns can be converted into balanced
A. P. by
Adding number of rows
Adding number of columns
Increasing each cost in matrix
None of these
11) A basic feasible solution to the T. P. is said to be degenerate if number of
non-negative allocations is
m n 1 m n 1
m n 1 None of these
12) A.T.P. with m origins and n destinations and if ai is availability of ith origin
and bj is requirement of jth destination is said to be balanced T. P. if
Sai Sbj Sai Sbj
Sai Sbj None of these
13) In an A. P. if number of columns is equal to number of rows then
Dummy column is added Dummy row is added
Any column is deleted None of these
14) Processing n jobs through three machines B and C in the order ABC is
possible only when
min{Ai} max{Bi} min{Ci} max{Bi}
max{Ai} min{Bi} Both and
2. Solve the following L.P.P. by graphical method. 7
Maximum Z 6x1 11x2
Subject to 2x1 11x2 104
x1 2x2 76
x1 x2 0
Define transportation problem and assignment problem. 7
3. Four professors are capable of teaching any one of four different courses.
The average weekly preparation time (in hours) for each subject by each
professor is given below. 7
I II III IV
A 2 10 9 7
B 15 4 14 8
C 13 14 16 11
D 4 15 13 9
How to assign each professor, one and only one course so as to minimize
the total course preparation time for all four courses
Explain the procedure of finding an optimum sequencing of n jobs processed
through m machines. 7
4. Attempt any one of the following 14
There are seven jobs, each of which has to go through the Machines A and
B in the order AB. Processing times in hours are given
Job 1 2 3 4 5 6 7
Machine A 3 12 15 6 10 11 9
Machine B 8 10 10 6 12 1 3
Determine a sequence of these jobs that will minimize the total elapsed time T.
Describe Hungarian algorithm.
5. Attempt any one of the following 14
Find I.B.F.S. by V.A.M. and optimum solution by MODI.
I II III IV aj
A 15 10 17 18 2
B 16 13 12 13 6
C 12 17 20 11 7
bj 3 3 4 5 15
A firm manufactures two types of Products A and B and sells them at a profit
of Rs. 2 on type A and Rs. 3 on type B. Each product is processed on two
machines G and H. Type A requires 2 minutes of processing on G and 3
minutes on H. Type B requires one minute on G and one minute on H. The
machine G is available for 6 hours 40 minutes, while machine H is available
for 10 hours during any working day. Formulate this problem as an L.P.P.