# Download PTU M.Tech Mech Eng 1st Semester 38202 OPTIMIZATION TECHNIQUES Question Paper

Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech Mech Eng 1st Semester 38202 OPTIMIZATION TECHNIQUES Question Paper.

1 | M - 3 8 2 0 2 ( S 9 ) - 5 0 3
Roll No. Total No. of Pages : 03
Total No. of Questions : 08
M.Tech.(ME) (Sem.?1)
OPTIMIZATION TECHNIQUES
Subject Code : MME-501
M.Code : 38202
Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWENTY marks.

Q1. a) Explain the important characteristics of the industrial situation to which I.P. method
can be successfully applied. Illustrate application of these technique with a suitable
example.
b) A company sells two different products A and B the company makes a profit of Rs.
40 and Rs. 30 on two products respectively. They are produced by a common
production process and are sold in two different markets. The production process has
a capacity of 30,000 man hours. It takes 3 hours to produce a unit of A and 1 hour to
produce a unit of B. The maximum number of Units of A and B that can be sold in
the market are 8000 and 12,000 respectively. Formulate the above as linear
programming model.
Q2. A person require 10, 12 and 12 units of chemical A, B and C respectively for his garden.
A liquid product contains 5, 2 and 1 unit of A, B and C respectively per jar. A dry
product contains 1, 2 and 4 units of A, B and C per carton. If the liquid product sells for
Rs. 3 per jar and the dry product sells for Rs. 2 per carton. How many of these should be
purchased to minimize the cost and meet the requirement.
Q3. Obtain the initial solution by VAM and optimal solution by MODI method for the
transportation problem shown below :
A B C Supply
W1 5 4 6 65
W2 7 4 7 42
Demand W3 8 6 7 43

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1 | M - 3 8 2 0 2 ( S 9 ) - 5 0 3
Roll No. Total No. of Pages : 03
Total No. of Questions : 08
M.Tech.(ME) (Sem.?1)
OPTIMIZATION TECHNIQUES
Subject Code : MME-501
M.Code : 38202
Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWENTY marks.

Q1. a) Explain the important characteristics of the industrial situation to which I.P. method
can be successfully applied. Illustrate application of these technique with a suitable
example.
b) A company sells two different products A and B the company makes a profit of Rs.
40 and Rs. 30 on two products respectively. They are produced by a common
production process and are sold in two different markets. The production process has
a capacity of 30,000 man hours. It takes 3 hours to produce a unit of A and 1 hour to
produce a unit of B. The maximum number of Units of A and B that can be sold in
the market are 8000 and 12,000 respectively. Formulate the above as linear
programming model.
Q2. A person require 10, 12 and 12 units of chemical A, B and C respectively for his garden.
A liquid product contains 5, 2 and 1 unit of A, B and C respectively per jar. A dry
product contains 1, 2 and 4 units of A, B and C per carton. If the liquid product sells for
Rs. 3 per jar and the dry product sells for Rs. 2 per carton. How many of these should be
purchased to minimize the cost and meet the requirement.
Q3. Obtain the initial solution by VAM and optimal solution by MODI method for the
transportation problem shown below :
A B C Supply
W1 5 4 6 65
W2 7 4 7 42
Demand W3 8 6 7 43

2 | M - 3 8 2 0 2 ( S 9 ) - 5 0 3
Q4. Five machine are to be located in the machine shop. There are five possible locations in
which the machine can be located. C
ij
the cost of placing i in place j is given in the table
below.
Place
1 2 3 4 5
1 15 10 25 25 10
2 1 8 10 20 2
Machine 3 8 9 17 20 10
4 14 10 25 27 15
5 10 8 25 27 12

It is required to place the machines at suitable place so as to minimize the total cost.
a) Formulate an L.P. model to find an optimal assignment.
b) Solve the problem by assignment technique of L.P.
Q5. Consider the following table :
0 m p
Activity Predecessor Times in Weeks
Activity t t t
A - 2 3 10
B - 2 3 4
C A 1 2 3
D A 4 6 14
E B 4 5 12
F C 3 4 5
G D,E 1 1 7

a) Draw the network diagram path.
b) Find the critical path and variance of each event.
c) What is the probability that the project will be completed in 16 weeks?
Q6. a) What is dynamic programming? Write step by step procedure to solve a general
problem by D.P.
b) Write the algorithm for Fibonacci search method.
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1 | M - 3 8 2 0 2 ( S 9 ) - 5 0 3
Roll No. Total No. of Pages : 03
Total No. of Questions : 08
M.Tech.(ME) (Sem.?1)
OPTIMIZATION TECHNIQUES
Subject Code : MME-501
M.Code : 38202
Time : 3 Hrs. Max. Marks : 100

INSTRUCTIONS TO CANDIDATES :
1. Attempt any FIVE questions out of EIGHT questions.
2. Each question carries TWENTY marks.

Q1. a) Explain the important characteristics of the industrial situation to which I.P. method
can be successfully applied. Illustrate application of these technique with a suitable
example.
b) A company sells two different products A and B the company makes a profit of Rs.
40 and Rs. 30 on two products respectively. They are produced by a common
production process and are sold in two different markets. The production process has
a capacity of 30,000 man hours. It takes 3 hours to produce a unit of A and 1 hour to
produce a unit of B. The maximum number of Units of A and B that can be sold in
the market are 8000 and 12,000 respectively. Formulate the above as linear
programming model.
Q2. A person require 10, 12 and 12 units of chemical A, B and C respectively for his garden.
A liquid product contains 5, 2 and 1 unit of A, B and C respectively per jar. A dry
product contains 1, 2 and 4 units of A, B and C per carton. If the liquid product sells for
Rs. 3 per jar and the dry product sells for Rs. 2 per carton. How many of these should be
purchased to minimize the cost and meet the requirement.
Q3. Obtain the initial solution by VAM and optimal solution by MODI method for the
transportation problem shown below :
A B C Supply
W1 5 4 6 65
W2 7 4 7 42
Demand W3 8 6 7 43

2 | M - 3 8 2 0 2 ( S 9 ) - 5 0 3
Q4. Five machine are to be located in the machine shop. There are five possible locations in
which the machine can be located. C
ij
the cost of placing i in place j is given in the table
below.
Place
1 2 3 4 5
1 15 10 25 25 10
2 1 8 10 20 2
Machine 3 8 9 17 20 10
4 14 10 25 27 15
5 10 8 25 27 12

It is required to place the machines at suitable place so as to minimize the total cost.
a) Formulate an L.P. model to find an optimal assignment.
b) Solve the problem by assignment technique of L.P.
Q5. Consider the following table :
0 m p
Activity Predecessor Times in Weeks
Activity t t t
A - 2 3 10
B - 2 3 4
C A 1 2 3
D A 4 6 14
E B 4 5 12
F C 3 4 5
G D,E 1 1 7

a) Draw the network diagram path.
b) Find the critical path and variance of each event.
c) What is the probability that the project will be completed in 16 weeks?
Q6. a) What is dynamic programming? Write step by step procedure to solve a general
problem by D.P.
b) Write the algorithm for Fibonacci search method.
3 | M - 3 8 2 0 2 ( S 9 ) - 5 0 3
Q7. Solve the following game by the principle of dominance :
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 ?1 1 2
4 4 3 4 ?5 2 2
5 4 3 3 ?2 2 2

Q8. Find the minimum of the function using the Newton-Raphson method with the starting
point ?1 = 0.1. Use ? = 0.01 for checking the convergence.
f ( ?)
1
2
0.75 1
= 0.65 0.65 tan
1
?
? ? ?
? ? ?

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page of Answer sheet will lead to UMC case against the Student.

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