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Monday, September 5, 2016



Roll No.
Total No. of Questions : 07
B.Com(Sem.–3rd)
OPERATION RESEARCH
Subject Code : BCOP-304
Paper ID : [B1127]
Time : 3 Hrs.                                        
INSTRUCTION TO CANDIDATES :
1. Section –A, is Compulsory.
2. Attempt any four questions from Section-B.

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.
                  

J1
J2
J3
J4
J5
W1
8
4
2
6
1
W2
0
9
5
5
4
W3
3
8
9
2
6
W4
4
3
1
0
3
W5
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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