Download PTU. I.K. Gujral Punjab Technical University (IKGPTU) M.Tech. CAD-CAM 1st Semester 23511 OPTIMIZATION TECHNIQUES Question Paper.

1 | M-23511 (S9)-1433

Roll No. Total No. of Pages : 03
Total No. of Questions : 08
OPTIMIZATION TECHNIQUES
Subject Code : ME-507
M.Code : 23511
Time : 3 Hrs. Max. Marks : 100

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

1. Solve the following L.P. problem using Big-M method.
Maximize Z = 2x
1
+ 3x
2
+ 4x
3

Subjected to 3x
1
+ x
2
+ 4x
3
? 600
2x
1
+ 4x
2
+ 2x
3
? 480
2x
1
+ 3x
2
+ 3x
3
= 540
x
1
, x
2
, x
3
? 0
2. Use two-phase simplex method to :
Maximize Z = 3x
1
+ 2x
2
+ 4x
3

Subjected to 5x
1
+ 7x
2
+ 4x
3
? 7
?4x
1
+ 7x
2
+ 5x
3
? ?2
3x
1
+ 4x
2
? 6x
3
? 29/7
x
1
, x
2
, x
3
? 0
3. Explain the following in the context of transportation problem
a. Stepping stone method
b. Modified distribution method
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1 | M-23511 (S9)-1433

Roll No. Total No. of Pages : 03
Total No. of Questions : 08
OPTIMIZATION TECHNIQUES
Subject Code : ME-507
M.Code : 23511
Time : 3 Hrs. Max. Marks : 100

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

1. Solve the following L.P. problem using Big-M method.
Maximize Z = 2x
1
+ 3x
2
+ 4x
3

Subjected to 3x
1
+ x
2
+ 4x
3
? 600
2x
1
+ 4x
2
+ 2x
3
? 480
2x
1
+ 3x
2
+ 3x
3
= 540
x
1
, x
2
, x
3
? 0
2. Use two-phase simplex method to :
Maximize Z = 3x
1
+ 2x
2
+ 4x
3

Subjected to 5x
1
+ 7x
2
+ 4x
3
? 7
?4x
1
+ 7x
2
+ 5x
3
? ?2
3x
1
+ 4x
2
? 6x
3
? 29/7
x
1
, x
2
, x
3
? 0
3. Explain the following in the context of transportation problem
a. Stepping stone method
b. Modified distribution method
2 | M-23511 (S9)-1433

4. Using the following cost matrix, determine optimal job assignment and the associated
cost :

Machinists
Jobs
1 2 3 4 5
A 10 3 3 2 8
B 9 7 8 2 7
C 7 5 6 2 4
D 3 5 8 2 4
E 9 10 9 6 10

5. A drug manufacturing concern has ten medical representative working in three sales
areas. The profitability for each representative in three sales area is as follows :
No. of Representative 0 1 2 3 4 5 6 7 8 9 10
Profitability
(thousand in
rupees)
Area 1 15 22 30 38 45 48 54 60 65 70 70
Area 2 26 35 40 46 55 62 70 76 83 90 95
Area 3 30 38 44 50 60 65 72 80 85 90 85
Determine the optimum allocation of medical representative in order to maximize the
profit. What will be the optimum allocation if the number of representative available at
present is only six?
6. Semi-finished components arrive at a workstation of an assembly line at an average rate
of Rs. 2 per minute, poisson distributed. A machine is to be installed at this workstation
for the specific operation. Three alternative machines P,Q and R are available. The
characteristics of the machine are given below. Whenever a component is idle, awaiting
the machine to get free, the cost is estimated at Rs.18 per minute. Using the concept of
single channel queue system and considering all relevant costs, recommend the machine
that would be the best for this work station.
Machine P Q R
Fixed Costs (Rs/Minute) 36 60 90
Variable Costs (Rs/minute) 18 15 8
Processing rate (Units/minutes) 3 6 12

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1 | M-23511 (S9)-1433

Roll No. Total No. of Pages : 03
Total No. of Questions : 08
OPTIMIZATION TECHNIQUES
Subject Code : ME-507
M.Code : 23511
Time : 3 Hrs. Max. Marks : 100

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

1. Solve the following L.P. problem using Big-M method.
Maximize Z = 2x
1
+ 3x
2
+ 4x
3

Subjected to 3x
1
+ x
2
+ 4x
3
? 600
2x
1
+ 4x
2
+ 2x
3
? 480
2x
1
+ 3x
2
+ 3x
3
= 540
x
1
, x
2
, x
3
? 0
2. Use two-phase simplex method to :
Maximize Z = 3x
1
+ 2x
2
+ 4x
3

Subjected to 5x
1
+ 7x
2
+ 4x
3
? 7
?4x
1
+ 7x
2
+ 5x
3
? ?2
3x
1
+ 4x
2
? 6x
3
? 29/7
x
1
, x
2
, x
3
? 0
3. Explain the following in the context of transportation problem
a. Stepping stone method
b. Modified distribution method
2 | M-23511 (S9)-1433

4. Using the following cost matrix, determine optimal job assignment and the associated
cost :

Machinists
Jobs
1 2 3 4 5
A 10 3 3 2 8
B 9 7 8 2 7
C 7 5 6 2 4
D 3 5 8 2 4
E 9 10 9 6 10

5. A drug manufacturing concern has ten medical representative working in three sales
areas. The profitability for each representative in three sales area is as follows :
No. of Representative 0 1 2 3 4 5 6 7 8 9 10
Profitability
(thousand in
rupees)
Area 1 15 22 30 38 45 48 54 60 65 70 70
Area 2 26 35 40 46 55 62 70 76 83 90 95
Area 3 30 38 44 50 60 65 72 80 85 90 85
Determine the optimum allocation of medical representative in order to maximize the
profit. What will be the optimum allocation if the number of representative available at
present is only six?
6. Semi-finished components arrive at a workstation of an assembly line at an average rate
of Rs. 2 per minute, poisson distributed. A machine is to be installed at this workstation
for the specific operation. Three alternative machines P,Q and R are available. The
characteristics of the machine are given below. Whenever a component is idle, awaiting
the machine to get free, the cost is estimated at Rs.18 per minute. Using the concept of
single channel queue system and considering all relevant costs, recommend the machine
that would be the best for this work station.
Machine P Q R
Fixed Costs (Rs/Minute) 36 60 90
Variable Costs (Rs/minute) 18 15 8
Processing rate (Units/minutes) 3 6 12

3 | M-23511 (S9)-1433

7. An inventory manager wishes to determine (a) the expected (mean) demand of a
particular item, and (b) the record lead time. This information is needed to determine,
how far in advance, to record, before the stock level is reduced to zero. However the
probability distribution for lead time and demand per day is given as under :
Lead Time (days) 1 2 3 Demand/Day 1 2 3 4
Probability 0.5 0.3 0.2 Probability 0.1 0.3 0.4 0.2
Simulate the problem for 10 days, to estimate the demand during lead time. When the
orders should be planned? Assume replenishment level as 4 units. Random numbers
22,17,08,49,29,57,05,10,81,75, 45,37,28,87,56,15,41.
8. Write short note on :
a. Sensitivity analysis
b. Generation of Random numbers

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