# PTU B.Tech Mechanical Engineering 6th Semester May 2019 71264 OPTIMIZATION TECHNIQUES Question Papers

PTU Punjab Technical University B-Tech May 2019 Question Papers 6th Semester Mechanical Engineering (MECH)

Roll No.
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(ME) (E-I 2011 Onwards) (Sem.?6)
OPTIMIZATION TECHNIQUES
Subject Code : DE/ME-3.2
M.Code : 71264
Time : 3 Hrs. Max. Marks : 60
INSTRUCTION TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying T EN marks each and students
have to attempt any T WO questions.

SECTION-A
1.

a) List three steps for critical path analysis.

b) What is duality in LP?

c) Name the two fundamental conditions that are the basis of the simplex method.

d) What is proportionality in linear programming?

e) Name different methods to solve transportation problem.

f) Name the three major constituents of a queuing model.

g) Explain term Pessimistic Time Estimate in PERT/CPM.

h) List two uses of replacement model.

i) Name assumptions made in linear programming model.

j) What are the applications of dynamic programming?

SECTION B
2.
Explain Big M method.
3.
Using Graphical Method Maximize Z = 3X1 + 4X2

subject to :
5X1 + 4X2 200;

3X1 + 5X2 150;

5X1 + 4X2 100;

8X1 + 4X2 80;

X1, X2 0
1 | M - 7 1 2 6 4

( S 2 ) - 1 6 1 3

4. A company has one surplus truck in each of the cities A, B, C, D and E and one deficit
truck in each of the cities 1, 2, 3, 4, 5, and 6. The distance between the cities in kilometre is
shown in matrix below. Find the assignment of the trucks from cities in surplus to cities in
deficit so that the total distance covered by vehicles is minimum.

1
2
3
4
5
6
A
12
10
15
22
18
8
B
10
18
25
15
16
12
C
11
10
3
8
5
9
D
6
14
10
13
13
12
E
8
12
11
7
13
10

5.
Find the cost per period of individual replacement policy of an installation of 300 lights
bulbs, given the following :

a) Cost of replacing individual bulb is Rs. 2.

b) Conditional probability of failure :

Week No.
0
1
2
3
4
Conditional probability of failure :
0
0.1
0.3
0.7
1

Also calculate the number of light bulbs that would fail during each of the four weeks.
6.
State assumptions made in transportation model.

SECTION-C
7.
The cost of a machine is Rs. 6100/- and its scrap value is Rs. 100. The maintenance costs
found from experience are as follow :

Year
1
2
3
4
5
6
7
8
Maintenance Cost
100
250
400
600
900
1200
1600
2000

When should the machine be replaced?
8.
Discuss seven elements of queuing system.
9.
Explain the similarities and differences between CPM and PERT.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any