Roll No.
Total No. of Questions : 07
B.Com(Sem.–3rd)
OPERATION
RESEARCH
Subject
Code : BCOP304
Paper
ID : [B1127]
Time : 3 Hrs.
INSTRUCTION TO CANDIDATES :
1.
Section –A, is Compulsory.
2.
Attempt any four questions from SectionB.
Section
–A
Q.1.(a)
Define artificial variables and explain their significance.
(b)
Write the condition to determine the existence of unbounded solution of linear
pro gamming
problem in simplex method.
(c)
Write the dual of the following LP.
Min
z = 4x2 + 5x3
2x1
– x2 + 4x3 ≤ 3
2x2
– 5x3 ≥ 7
x1,
x3 ≥ 0
(d)
In a balanced transportation problem with m sources and n destinations what is
the number of nonbasic variables?
(e)
Define degeneracy in transportation problem. Explain briefly how the degeneracy
occurs in intermediate stages.
(f)
Check whether the following game possesses saddle point. If so, what is the
value of the game?
A
8

5

8

8

3

5

7

4

5

6

6

6

A
g)
Solve the following game using odds method:
B
1

3

2

1

(h)
Write the Fulkerson’s rule to number the nodes in a network diagram.
(i)
Define al the costs associated with the inventories.
(j)
A manufacturer has to supply his customer with 60 units of his product per
year. Shortages are not allowed and the storage cost amounts to Rs. 0.60 per
unit per year. The setup cost per un is Rs. 80. Find the optimum run size and
the minimum average yearly cost.
Section
–B
Q.2.(a).
The manager of an oil refinery must decide on the optimum mix of two possible
blending processes of which the input and output production runs are a follows.
Process Input Output
Crude
A Crude B Gasoline X Gasoline
Y
1 6 4 6
9
2 5 6 5 5
The
maximum amounts available of crude A and crude B are 250 units and 20 units
respectively. Market demand shows that atleast 150 units of gasoline X and
gasoline Y must be produced. The profits per production run from proces 1 and
process 2 are Rs. 4 and Rs. 5 respectively. Formulate the problem to maximize
the profit.
(b)
Write the mathematical formulation of transportation problem.
Q.3.Solve
the following linear programming problem by simplex method.
Maximize
z = 4x1 + 3x2 + 4x3 + 6x4
x1
+ 2x2 + 2x3 + 4x4 ≤ 80
2x1
+ 2x3+ x4 ≤ 60
3x1
+ 3x2 + x3 + x4 ≤ 80
x1,
x2, x3,x4 ≥ 0
Q.4.Find
the optimal solution of the transportation problem where the costs, the
capacities of the sources and the demands of the destinations are given in the
table below:
Destination
Source

1

2

3

4

Supply

1

23

27

16

18

30

2

12

17

20

51

40

3

22

28

12

32

53

Demand

23

27

16

18


Q.5.(a). Given the following data, determine
the least cost allocation of the available workers to the five jobs.

J_{1}

J_{2}

J_{3}

J_{4}

J_{5}

W_{1}

8

4

2

6

1

W_{2}

0

9

5

5

4

W_{3}

3

8

9

2

6

W_{4}

4

3

1

0

3

W_{5}

9

5

8

9

5

(b). Solve the following problem for the
salesman to determine the route covering the areas A, B, C,D and E so that he
total cost is minimum

A

B

C

D

E

A



2

5

7

1

B

6



3

8

2

C

8

7



4

7

D

12

4

6



5

E

1

3

2

8



Q.6.(a).
Solve the following game using the dominance rule
4

2

0

2

1

1

4

3

1

3

2

2

4

3

7

5

1

2

4

3

4

1

2

2

4

3

3

2

2

2

(b). Determine the optimal sequence of jobs
that minimizes the total time required in performing the following jobs on three
machines in the order ABC:
Processing time jobs
In
hours ) j1 j2 j3 j4 j5 j6 j7
Machine
A 10 8 12 6 9 11 9
Machine
B 6 4 6 5 3 4 2
Machine
C 8 7 5 9 10 6 5
Also
determine the total elapsed time and idle time for each machine.
Q.7.
The information about a project is give in the following table.
Activity

Predecessor Activity

Duration (weeks)

A



8

B



10

C



8

D

A

10

E

A

16

F

B,D

17

G

C

18

H

C

14

i

F,G

9

(i).
Draw the network for the above project.
(i).
Determine the critical path and the duration of the project.
(i).
Find all three types of floats.
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