B.Com. III (Semester (CBCS) Examination, 2018
Statistics (Paper II)
Advanced Statistics
Day and Date Saturday, 8-12-2018 Max. Marks 70
Time 10.30 a.m. to 1.00 p.m.
Instructions All questions are compulsory and carry equal marks.
Figures to the right indicate full marks.
Use of soundless calculators is allowed.
1. Choose the most appropriate alternatives of the following question. 14
The linear function of variables which is to be maximized or minimized is
called
constraints basic requirements
an objective function none of them
A constraint in an LP model restricts
value of the objective function
use of the available resources
values of the decision variables
all of the above
The feasible solution to an L.P.P.
Must satisfy all the constraints simultaneously
Need not satisfy all the constraints, only some of them
Must be a corner point of the feasible region
All of the above
The objective function for a L.P. model is 3x1 2x2, if x1 20 and x2 30,
what is the value of the objective function
0 6 50 120
Linear programming problem involving only two variables only can be solved by
big M method simplex method
graphical method none of the these
If the value of an objective function Z can be increased or decreased
indefinitely, such solution is called
bounded solution feasible solution
unbounded solution none of these
In the optimal simplex table cj zj 0 value indicates an existence of
an unbounded solution cycling
alternative solution none of these
In a non-degenerate solution to T.P. with m rows and n columns, number
of allocated cell is
equal to m n 1 equal to m n 1
not equal to m n 1 none of these
An Assignment Problem is considered as a particular case of a Transportation
Problem because
the number of rows equals the number of columns
all xij 0 or 1
all rim conditions are 1
all of the above
10) In a sequencing, if smallest time for a job on two machines M1 and M2
belongs to M2 then that job has to be placed
in the middle in the starting
at the end none of these
11) Processing time Mij's and order of processing the jobs are
dependent negligible
independent none of these
12) In a sequencing the time involved in moving jobs from one machine to
another is
negligible positive number
significant none of them
13) If there are in jobs to be performed, one at a time, on each of m machines,
the possible sequences would be

14) The method used for solving an assignment problem is called
reduced matrix method Hungarian method
MODI method None of the above
Set P
*SLRCO63* SLR-CO 63
2. A manufacturer has two machines A and B. He manufactures two products
P and Q on these two machines. For manufacturing product P he has to
use machine A for 3 hours and machine B for 6 hours and for manufacturing
product Q he has to use machine A for 6 hours and machine B for 5 hours.
On each unit of P he earns Rs. 14 and on each unit of Q he earns Rs. 10.
How many units of P and Q should be manufactured to get the maximum
profit Each machine cannot be used for more than 2100 hours. Formulate
this as an L.P.P. 7
Write a procedure of matrix minima method. 7
3. Solve the following L.P.P graphically 7
Maximize Z 2x1 3x2
Such that x1 x2 1
3x1 x2 4
x1, x2 0.
Explain the standard form of an L.P.P. 7
4. Attempt any one of the following 14
Solve the following assignment problem so as to minimize the time (in days)
required to complete all the task.
Task
Person
1 2 3 4 5
aBCD
6 5 8 11 16
1 13 16 1 10
16 11 8 8 8
9 14 12 10 1
Write the steps of the algorithm for solving LPP by the Simplex method.
5. Attempt any one of the following 14
A machine operator has to perform three operations turning, threading and
knurling on a number of different jobs. The time required to perform these
operations (in minutes) for each job is known. Determine the order in which
the jobs should be processed in order to minimize the total time required to
perform all the jobs. Also find idle times for all operations. Also find idle time
for all operations.
Job Time for turning
(minutes)
Time for threading
(minutes)
Time for knurling
(minutes)
1 3 8 13
2 12 6 14
3 5 4 9
4 2 6 12
5 9 3 8
6 11 1 13
Solve the following L.P.P., by simplex method
Max Z 5x1 3x2
Subject to the constraints 3x1 5x2 15,
5x1 2x2 10,
where x1, x2 0