University Of Pune Question Paper
FYMCA (Engg. Faculty)
OPERATIONS RESEARCH
(Semester -II) (2008 Pattern) (510911)
MAY 2013 EXAMINATIONS
Time: 3 Hours] [Max. Marks : 70
Instructions to the candidates:
1) From Section – I answer (Q1 or Q2) and (Q3 or Q4) and (Q5 or Q6)
2) From Section –II ( Q7 or Q8) and ( Q9 or Q10) and (Q11 or Q12)
3) Answers to two sections should be written in separate answer books.
4) Neat diagrams must be drawn wherever necessary.
5) Assume suitable data, if necessary.
SECTION I
Q1) a) The ABC company produces two products: I and II. The raw material
requirements, space needed for storage, production rates, and selling prices for
those products are given in table.
Table: Production data for ABC company
Product
I II
Storage space (ft2
/unit) 4 5
Raw material (lb/unit) 5 3
Production rate (units/hr) 60 30
Selling price (Rs./unit) 13 11
The total amount of raw material available per day for both products is 1575 lb.
The total storage space for all products is 1500 ft2
, and a maximum of 7 hours per
day can be used for production.
All products manufactured are shipped out of the storage area at the end of the
day. Therefore, the two products must share the total raw material, storage space,
and production time. The company wants to determine how many units of each
product to produce per day to maximize its total income.
[8]
b) Write a short note on ‘Sensitivity Analysis’. [4]
OR
Q2) a) Solve the given LPP by simplex method.
Maximize z = 10x1 + 20x2
s.t. 5x1 + 3x2 ≤ 30
3x1 + 6x2 ≤ 36
2x1 + 5x2 ≤ 20
and x1, x2 ≥ 0
[8]
b) Construct a dual problem from the given primal.
Minimize z = x1 + x2 + x3
s.t. x1 - 3x2 + 4x3 = 5
x1 - 2x2 ≤ 3
2x2 – x3 ≥ 4 and x1, x2 ≥ 0, x3 is unrestricted.
[4]
[4366]-203 Page 2 of 4
Q3) a) Using Vogel’s Approximation Method, solve the following transportation
problem.
D1 D2 D3 D4
Available
O1 21 16 25 13 11
O2 17 18 14 23 13
O3 32 27 18 41 19
Requirement 6 10 12 15
[6]
b) Use MODI Method to check the optimality of the following transportation
problem.
A B C D Capacity
F1
19
5
30 50 10
2 7
F2
70 30 40
7
60
2 9
F3
40 8
8
70 20
10 18
Requirement 5 8 7 14
[6]
OR
Q4) a) Write a short note on ‘Transhipment model’. [4]
b) A marketing manager has 5 salesman and 5 districts. Considering the
capabilities of the salesman and nature of districts, the marketing manager
estimates of sales per month ( in hundreds of rupees) for each salesman in each
district would be as follows:
Job Machine
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 41 36 36
5 29 33 40 35 39
Find the assignment of salesman to districts that would result in the maximum
sales.
[8]
[4366]-203 Page 3 of 4
Q5) a) From the information given below draw network diagram and critical path. Find
the probability that the project will be completed within 55 days.
Activity to tm tp
1-2 4 6 8
2-3 5 7 15
2-4 4 8 12
3-6 15 20 25
3-5 10 18 26
4-6 8 9 16
5-7 4 8 12
6-7 1 2 3
7-8 6 7 8
[7]
b) Explain the steps of kruskal’s minimum spanning tree algorithm. [4]
OR
Q6) a) Write the steps of Floyd’s Algorithm. [4]
b) Compare CPM and PERT. [3]
c) Use Dijkstra’s algorithm to find the shortest route between node and every node
in the following network.
[4]
SECTION II
Q7) a) Use Branch and Bound method to solve following LPP.
Minimize z = 4x1 +3 x2
s.t. 5x1 + 3x2 ≥ 30,
x1 ≤ 4, x2 ≤ 6
and x1 , x2 ≥ 0,
x1, x2 are integers.
[7]
b) What is Goal programming? Explain two methods to solve goal programming
problem.
[5]
S4
S5 S2
S3
S1
5 1
15
10
2
8
3 4
[4366]-203 Page 4 of 4
OR
Q8) a) Write the different forecasting technique. Explain any one of them. [6]
b) A company is considering the allocation of Rs. 1, 50,000 advertising budget to
two magazines (A and B). Rated exposures per hundred rupees of advertising
expenditure are 1000 and 750 respectively for the two magazines; and it has been
forecast that on the average Rs.10 in sales results from each advertisement
exposures. Management has decided that no more than 75% of the advertising
budget can be expended in magazine A. The company has indicated that it would
likely to achieve exactly 1.5 million exposures from its advertising program.
Management’s objective is to allocate its money to advertising in such a way that
sales (Rs.) are maximized. Formulate the given Goal programming problem.
[6]
Q9) Analyze the decision problem using –
a) Laplace b) Minimax c) Savage d) Hurwicz criteria. The cost matrix for the
situation is :
S1 S2 S3 S4
A1 5 10 18 25
A2 8 7 12 23
A3 21 18 12 21
A4 30 22 19 15
Given : P(sj) = 1/4 and alpha = 0.5
[12]
OR
Q10) a) Explain Decision Making under certainty using AHP. [6]
b) What is decision making under risk? Explain expected value criterion. [6]
Q11) a) What is simulation modeling? Explain Monte carlo simulation. [5]
b) Explain the three most common methods for collecting observations in
simulation.
[6]
OR
Q12) a) Explain in brief generation of Random numbers. Generate three random numbers
based on multiplicative congruential method using b = 17, c = 111, m = 103,
seed = 7.
[7]
b) Define simulations. Explain Merits and Demerits of Simulation Technique.
FYMCA (Engg. Faculty)
OPERATIONS RESEARCH
(Semester -II) (2008 Pattern) (510911)
MAY 2013 EXAMINATIONS
Time: 3 Hours] [Max. Marks : 70
Instructions to the candidates:
2) From Section –II ( Q7 or Q8) and ( Q9 or Q10) and (Q11 or Q12)
3) Answers to two sections should be written in separate answer books.
4) Neat diagrams must be drawn wherever necessary.
5) Assume suitable data, if necessary.
SECTION I
Q1) a) The ABC company produces two products: I and II. The raw material
requirements, space needed for storage, production rates, and selling prices for
those products are given in table.
Table: Production data for ABC company
Product
I II
Storage space (ft2
/unit) 4 5
Raw material (lb/unit) 5 3
Production rate (units/hr) 60 30
Selling price (Rs./unit) 13 11
The total amount of raw material available per day for both products is 1575 lb.
The total storage space for all products is 1500 ft2
, and a maximum of 7 hours per
day can be used for production.
All products manufactured are shipped out of the storage area at the end of the
day. Therefore, the two products must share the total raw material, storage space,
and production time. The company wants to determine how many units of each
product to produce per day to maximize its total income.
[8]
b) Write a short note on ‘Sensitivity Analysis’. [4]
OR
Q2) a) Solve the given LPP by simplex method.
Maximize z = 10x1 + 20x2
s.t. 5x1 + 3x2 ≤ 30
3x1 + 6x2 ≤ 36
2x1 + 5x2 ≤ 20
and x1, x2 ≥ 0
[8]
b) Construct a dual problem from the given primal.
Minimize z = x1 + x2 + x3
s.t. x1 - 3x2 + 4x3 = 5
x1 - 2x2 ≤ 3
2x2 – x3 ≥ 4 and x1, x2 ≥ 0, x3 is unrestricted.
[4]
[4366]-203 Page 2 of 4
Q3) a) Using Vogel’s Approximation Method, solve the following transportation
problem.
D1 D2 D3 D4
Available
O1 21 16 25 13 11
O2 17 18 14 23 13
O3 32 27 18 41 19
Requirement 6 10 12 15
[6]
b) Use MODI Method to check the optimality of the following transportation
problem.
A B C D Capacity
F1
19
5
30 50 10
2 7
F2
70 30 40
7
60
2 9
F3
40 8
8
70 20
10 18
Requirement 5 8 7 14
[6]
OR
Q4) a) Write a short note on ‘Transhipment model’. [4]
b) A marketing manager has 5 salesman and 5 districts. Considering the
capabilities of the salesman and nature of districts, the marketing manager
estimates of sales per month ( in hundreds of rupees) for each salesman in each
district would be as follows:
Job Machine
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 41 36 36
5 29 33 40 35 39
Find the assignment of salesman to districts that would result in the maximum
sales.
[8]
[4366]-203 Page 3 of 4
Q5) a) From the information given below draw network diagram and critical path. Find
the probability that the project will be completed within 55 days.
Activity to tm tp
1-2 4 6 8
2-3 5 7 15
2-4 4 8 12
3-6 15 20 25
3-5 10 18 26
4-6 8 9 16
5-7 4 8 12
6-7 1 2 3
7-8 6 7 8
[7]
b) Explain the steps of kruskal’s minimum spanning tree algorithm. [4]
OR
Q6) a) Write the steps of Floyd’s Algorithm. [4]
b) Compare CPM and PERT. [3]
c) Use Dijkstra’s algorithm to find the shortest route between node and every node
in the following network.
[4]
SECTION II
Q7) a) Use Branch and Bound method to solve following LPP.
Minimize z = 4x1 +3 x2
s.t. 5x1 + 3x2 ≥ 30,
x1 ≤ 4, x2 ≤ 6
and x1 , x2 ≥ 0,
x1, x2 are integers.
[7]
b) What is Goal programming? Explain two methods to solve goal programming
problem.
[5]
S4
S5 S2
S3
S1
5 1
15
10
2
8
3 4
[4366]-203 Page 4 of 4
OR
Q8) a) Write the different forecasting technique. Explain any one of them. [6]
b) A company is considering the allocation of Rs. 1, 50,000 advertising budget to
two magazines (A and B). Rated exposures per hundred rupees of advertising
expenditure are 1000 and 750 respectively for the two magazines; and it has been
forecast that on the average Rs.10 in sales results from each advertisement
exposures. Management has decided that no more than 75% of the advertising
budget can be expended in magazine A. The company has indicated that it would
likely to achieve exactly 1.5 million exposures from its advertising program.
Management’s objective is to allocate its money to advertising in such a way that
sales (Rs.) are maximized. Formulate the given Goal programming problem.
[6]
Q9) Analyze the decision problem using –
a) Laplace b) Minimax c) Savage d) Hurwicz criteria. The cost matrix for the
situation is :
S1 S2 S3 S4
A1 5 10 18 25
A2 8 7 12 23
A3 21 18 12 21
A4 30 22 19 15
Given : P(sj) = 1/4 and alpha = 0.5
[12]
OR
Q10) a) Explain Decision Making under certainty using AHP. [6]
b) What is decision making under risk? Explain expected value criterion. [6]
Q11) a) What is simulation modeling? Explain Monte carlo simulation. [5]
b) Explain the three most common methods for collecting observations in
simulation.
[6]
OR
Q12) a) Explain in brief generation of Random numbers. Generate three random numbers
based on multiplicative congruential method using b = 17, c = 111, m = 103,
seed = 7.
[7]
b) Define simulations. Explain Merits and Demerits of Simulation Technique.
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