Download MU-(University of Mumbai or University of Bombay) MCA (Master of Computer Application) 2019 May 3rd Sem 56104 Operation Research Previous Question Paper
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
59166 Page 1 of 3
Duration 3 hours Total 100 marks
N.B: (1) Question No. 1 is compulsory.
(2) Attempt any four out of remaining six questions.
(3) Assume any necessary data but justify the same.
(4) Figures to the right indicate marks.
(5) Use of scientific calculator is allowed.
1 a) XYZ farm is engaged in breeding cows. The cows are fed on various products grown on the farm.
Because of the need to ensure certain nutrient constituents, it is necessary to buy additional one or two
products, which we shall call A and B. The nutrient constituents (vitamins and proteins) in each unit
of product are given below.
Nutrient
Constituents
Nutrient Constituents Minimum requirements of
nutrient constituents A B
1 36 6 108
2 3 12 36
3 20 10 100
Product A costs Rs. 20 per unit and product B costs Rs 40 per unit. Determine how much of products
A and B must be purchased so as to provide the cow nutrients not less than the minimum required, at
the lowest cost. Solve the LP problem graphically. [10]
b) The following is the activity list of a project with time estimates [10]
Activity Time(days)
Optimistic Most likely Pessimistic
1-2 (A) 6 6 24
1-3 (B) 6 12 18
1-4 (C) 12 12 30
2-5 (D) 6 6 6
3-5 (E) 12 30 48
4-6 (F) 12 30 42
5-6 (G) 18 30 54
Draw a network. Find expected duration and variance for each activity
What is the probability of the project is not being completed in 80 days?
[Given, for SNV, Z=0.69, area between mean and value of Z is 0.2549].
2 a) Solve the following LPP by simplex method. [10]
Maximize: Z= 10x1+6x2+4x3
Subject to: x1+x2+x3 ? 100
10x1+4x2+5x3 ? 600
2x1+2x2+6x3 ? 300
x1, x2,x3 ? 0
Paper / Subject Code: 56104 / Operation Research
8ABC7E38817571ADA7806931AD43FABA
FirstRanker.com - FirstRanker's Choice
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
59166 Page 1 of 3
Duration 3 hours Total 100 marks
N.B: (1) Question No. 1 is compulsory.
(2) Attempt any four out of remaining six questions.
(3) Assume any necessary data but justify the same.
(4) Figures to the right indicate marks.
(5) Use of scientific calculator is allowed.
1 a) XYZ farm is engaged in breeding cows. The cows are fed on various products grown on the farm.
Because of the need to ensure certain nutrient constituents, it is necessary to buy additional one or two
products, which we shall call A and B. The nutrient constituents (vitamins and proteins) in each unit
of product are given below.
Nutrient
Constituents
Nutrient Constituents Minimum requirements of
nutrient constituents A B
1 36 6 108
2 3 12 36
3 20 10 100
Product A costs Rs. 20 per unit and product B costs Rs 40 per unit. Determine how much of products
A and B must be purchased so as to provide the cow nutrients not less than the minimum required, at
the lowest cost. Solve the LP problem graphically. [10]
b) The following is the activity list of a project with time estimates [10]
Activity Time(days)
Optimistic Most likely Pessimistic
1-2 (A) 6 6 24
1-3 (B) 6 12 18
1-4 (C) 12 12 30
2-5 (D) 6 6 6
3-5 (E) 12 30 48
4-6 (F) 12 30 42
5-6 (G) 18 30 54
Draw a network. Find expected duration and variance for each activity
What is the probability of the project is not being completed in 80 days?
[Given, for SNV, Z=0.69, area between mean and value of Z is 0.2549].
2 a) Solve the following LPP by simplex method. [10]
Maximize: Z= 10x1+6x2+4x3
Subject to: x1+x2+x3 ? 100
10x1+4x2+5x3 ? 600
2x1+2x2+6x3 ? 300
x1, x2,x3 ? 0
Paper / Subject Code: 56104 / Operation Research
8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
59166 Page 2 of 3
b) Find the initial basic feasible solution of the following Transportation Problem by Least Cost
Method. [10]
To
From
Supply
2
7 4 5
3
3 1 8
5 4 7 7
1 6 2 14
Demand 7 9 18
3 a) Solve the following using big M method. [10]
Maximize Z = 3x1-x2
Subject to the constraints 2x1+x2 ? 2
x1+3x2 ? 3
x2 ? 4
x1, x2 ? ?0
(b) The captain of a cricket team has to allot the five middle bating positions to five batsmen. The
average runs scored by each batsman at these positions are as follows. [10]
Batsman Batting Position
I II III IV V
P
Q
R
S
T
40
42
50
20
58
40
30
48
19
60
35
16
40
20
59
25
25
60
18
55
50
27
50
25
53
Find the assignment of batsmen to positions which will give the maximum number of runs.
4 a) Solve the LPP by Dual Simplex Method. [10]
Minimize Z = 2x2+5x3
Subject to x1+x2 ? 2
2x1+x2+6x3 ? 10
x1-x2+x3 ? 4
x1, x2 ,x3 ?0
b) Six jobs have to be processed at three machines A, B, C in order ACB. The time(in hrs) taken by
each job on each machine is indicated below. [10]
Jobs I II III IV V VI
M/C A 12 8 7 11 10 5
M/C B 7 10 9 6 10 5
M/C C 3 4 2 5 5 4
Determine the sequence for the jobs so as to minimize the processing time. Determine the total
elapsed and idle time of each machine.
Paper / Subject Code: 56104 / Operation Research
8ABC7E38817571ADA7806931AD43FABA
FirstRanker.com - FirstRanker's Choice
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
59166 Page 1 of 3
Duration 3 hours Total 100 marks
N.B: (1) Question No. 1 is compulsory.
(2) Attempt any four out of remaining six questions.
(3) Assume any necessary data but justify the same.
(4) Figures to the right indicate marks.
(5) Use of scientific calculator is allowed.
1 a) XYZ farm is engaged in breeding cows. The cows are fed on various products grown on the farm.
Because of the need to ensure certain nutrient constituents, it is necessary to buy additional one or two
products, which we shall call A and B. The nutrient constituents (vitamins and proteins) in each unit
of product are given below.
Nutrient
Constituents
Nutrient Constituents Minimum requirements of
nutrient constituents A B
1 36 6 108
2 3 12 36
3 20 10 100
Product A costs Rs. 20 per unit and product B costs Rs 40 per unit. Determine how much of products
A and B must be purchased so as to provide the cow nutrients not less than the minimum required, at
the lowest cost. Solve the LP problem graphically. [10]
b) The following is the activity list of a project with time estimates [10]
Activity Time(days)
Optimistic Most likely Pessimistic
1-2 (A) 6 6 24
1-3 (B) 6 12 18
1-4 (C) 12 12 30
2-5 (D) 6 6 6
3-5 (E) 12 30 48
4-6 (F) 12 30 42
5-6 (G) 18 30 54
Draw a network. Find expected duration and variance for each activity
What is the probability of the project is not being completed in 80 days?
[Given, for SNV, Z=0.69, area between mean and value of Z is 0.2549].
2 a) Solve the following LPP by simplex method. [10]
Maximize: Z= 10x1+6x2+4x3
Subject to: x1+x2+x3 ? 100
10x1+4x2+5x3 ? 600
2x1+2x2+6x3 ? 300
x1, x2,x3 ? 0
Paper / Subject Code: 56104 / Operation Research
8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
59166 Page 2 of 3
b) Find the initial basic feasible solution of the following Transportation Problem by Least Cost
Method. [10]
To
From
Supply
2
7 4 5
3
3 1 8
5 4 7 7
1 6 2 14
Demand 7 9 18
3 a) Solve the following using big M method. [10]
Maximize Z = 3x1-x2
Subject to the constraints 2x1+x2 ? 2
x1+3x2 ? 3
x2 ? 4
x1, x2 ? ?0
(b) The captain of a cricket team has to allot the five middle bating positions to five batsmen. The
average runs scored by each batsman at these positions are as follows. [10]
Batsman Batting Position
I II III IV V
P
Q
R
S
T
40
42
50
20
58
40
30
48
19
60
35
16
40
20
59
25
25
60
18
55
50
27
50
25
53
Find the assignment of batsmen to positions which will give the maximum number of runs.
4 a) Solve the LPP by Dual Simplex Method. [10]
Minimize Z = 2x2+5x3
Subject to x1+x2 ? 2
2x1+x2+6x3 ? 10
x1-x2+x3 ? 4
x1, x2 ,x3 ?0
b) Six jobs have to be processed at three machines A, B, C in order ACB. The time(in hrs) taken by
each job on each machine is indicated below. [10]
Jobs I II III IV V VI
M/C A 12 8 7 11 10 5
M/C B 7 10 9 6 10 5
M/C C 3 4 2 5 5 4
Determine the sequence for the jobs so as to minimize the processing time. Determine the total
elapsed and idle time of each machine.
Paper / Subject Code: 56104 / Operation Research
8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA8ABC7E38817571ADA7806931AD43FABA
59166 Page 3 of 3
5 a) Write short notes on the following. [10]
(i) Different costs associated with inventory problem.
(ii) Dual of a primal in LPP.
b) Solve using Gomory?s cutting plane method. [10]
Maximize z=x1+2x2
Subject to: 3x1+2x2 ? 5
x2 ? 2
x1, x2 ?0 and integer.
6 a) Explain the following. [10]
(i) Branch and bound method of solving Traveling Salesman Problem.
(ii) Pure and mixed strategies in Game Theory.
b) The following mortality rates have been observed for a certain type of fuse. There are 1000 fuses in
use, and it costs Rs 5 to replace an individual fuse. If all fuses were replaced simultaneously it would
cost Rs 1.25 per fuse. It is proposed to replace all fuses at fixed interval of time, whether or not they
have burnt out, and to continue replacing out fuses as and when they fail. At what interval the group
replacement should be made? Also prove that this optimum policy is superior to the straightforward
policy of replacing each fuse only when it fails. [10]
Week 1 2 3 4 5
% failing at the end of the week 5 15 35 75 100
7 a) A small assembly plant assembles PCs through 9 interlinked activities. The time duration for
which is given below.
Activity 1-2 1-3 1-4 2-5 3-6 3-7 4-6 5-8 6-9 7-8 8-9
Duration 2 2 1 4 8 5 3 1 5 4 3
Draw a network for it. Tabulate total float, free float and independent float. [10]
b) Solve the following game by using the principle of dominance. [10]
______________________
Player B
Player A
I II III IV V VI
1 4 2 0 2 1 1
2 4 3 1 3 2 2
3 4 3 7 -5 1 2
4 4 3 4 -1 2 2
5 4 3 3 -2 2 2
Paper / Subject Code: 56104 / Operation Research
8ABC7E38817571ADA7806931AD43FABA
FirstRanker.com - FirstRanker's Choice
This post was last modified on 05 February 2020