B.E. (Civil) SYSTEMS APPROACH IN CIVIL ENGINEERING (2008 Pattern) (Sem. – I) (Elective – I)
Time: 3 Hours] 
[Max. Marks : 100
Instructions to the candidates:
1) Answer three questions from sectionI and three questions from sectionII.
2) Answers to the two sections should be written in separate books.
3) Neat diagrams must be drawn wherever necessary.
4) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed.
5) Assume suitable data, if necessary.
SECTION – I
QI) a) Minimize Z = 4x_{l} + x_{2}
Subject to 3x_{l} + x_{2} = 3
4x_{l} + 3x_{2} > 6
x_{l} + 2x_{2} < 3
x_{l5} x_{2} > 0
[IP] 
Use Big M method.
b) What is degeneracy in LPP? How is it resolved?
OR
Q2) a) What is dual LPP? When is it preferable to solve dual LPP? [4]
b)
[IP] 
Applying the principle of duality, solve the following LPP.
Maximize Z = 3x_{x} + 2x_{2} Subject to Xj + x_{2} > I
^{X}1 ^{+ X}2 ‘ ^{7} Xj + 2x_{2} < 10
^{X}2 ‘ ^{3} x_{j5} X_{2} > 0
Q3) A construction material is to be transported from 4 sources to 5 sites. The quantity available at sources and quantities required at sites are given below. The unit transportation costs are also given in the table below : [18]
Sources  Sites  Quantity
Available 

1 
2 
3 
4 
5 

A 
9 
10 
11 
2 
21 
20 
B 
7 
14 
9 
3 
7 
40 
C 
22 
11 
17 
9 
14 
120 
D 
12 
15 
6 
16 
5 
120 
Demands 
20 
40 
60 
80 
100 
Find the initial feasible solution by Voqel’s Aproximation Method (VAM) and using the initial solution obtained by VAM, find the distribution policy which will minimize the cost of transportation.
OR
Q4) a) A company has to assign five jobs to five employees such that each employee is assigned to one job. The time in hours each employee may take to perform each job is given in the table below. How should the job be assigned to the employees to minimize the total man hours? [10]
Employees

b) How will you use Assignment model for solving a maximization problem?
[4]
c) How will you solve a transportation problem if it is degenerate? [4]
Q5) A builder has 4 money units which he wishes to invest in projects A, B and
 The expected returns from the three projects for each level of investment are given below. Use dynamic programming to obtain the best allocation to maximize the overall returns. [IT]
Investment in money units 
Returns from projects 

A 
B 
C 

0 
0 
0 
0 
1 
7 
8 
9 
2 
25 
20 
15 
3 
30 
36 
19 
4 
38 
44 
30 
Explain the following terms used in dynamic programming. [T]
i)
Bellman’s principle of optimality.
ii) Stages and states.
Explain advantages and limitations of Dynamic Programming. [T] State any four different applications of dynamic programming. [4]
SECTION – II
Define the terms : [T]
i) Global and local optima.
ii) Hessian matrix.
Write a short note on ‘Non Linear Programming’. [3]
Verify whether the following functions are convex or concave. [9]
i) J(x) = 2×3 – 8x 2
ii) Xx) = 2x_{j} x_{2}
iii) f(x) = 2x^{R} + 8x^{2} + 5x
OR
Q8) a) 
Use the method of Lagrangian multiplier to [8]
Maximise Z = 6x_{x} + 8x_{2} – x 2 – x 2
Subject to 4x_{x} + 3x_{2} = 16 3Xj + 5x_{2} = 15 Where x_{v} x_{2} > 0.
b) Solve the following problem by Golden Section method. Maximise f (x) = 48x – 60x^{2} + x^{3} with n = 6 and within the range @0 to 1). [10]
Q9) a) What are the main elements of a queueing system? Explain any two of them. [6]
b) What is the need fo simulation? How can you use Monte Carlo simulation for industrial problems? [4]
c) Find the sequence for the following eight jobs that will minimise the total elapsed time for the completion of all the jobs. Each job is processed in the order CAB. [6]
Jobs 
1 
2 
3 
4 
5 
6 
7 
8 

Times in 
A 
3 
5 
6 
5 
6 
7 
4 
2 
Machine 
B 
9 
10 
8 
8 
12 
12 
11 
10 
C 
10 
8 
7 
9 
7 
10 
12 
11 
Also find the idle time for machines.
OR
QI 0) a) Customer arrive at a bank counter manned by a single cashier according to poisson’s distribution with mean arrival rate 5 customers/hour. The cashier attends the customers as first come first served basis at an average rate of 9 customers/hour with the service time. [8]
Find :
i) The probability of the number of arrivals (0 through 5).
ii) Probability that the queueing system is idle.
iii) Probability associated with the number of customers (0 through 5) in the queueing system.
iv) The time a customer expect to spend in the queue.
b) Give any three different examples of sequencing problems in day to day life. Also discuss the five cases in sequencing problem. [8]
QII) a) Define following terms :
i) Game.
ii) Pure strategy.
iii) Mixed strategy.
iv) Zero sum game.
b) Obtain value of following game. X Y
A B
c) The maintenance cost and resale value per year for an excavator is given below : [10]
Year 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Mainte. cost 
40000 
42000 
44000 
46000 
48000 
50000 
53000 
57000 
62000 
67000 
Resale value 
230000 
220000 
210000 
200000 
180000 
160000 
140000 
120000 
100000 
70000 
The purchase price of the excavator is Rs.2,50,000/ Find the year in which replacement is to be carried out.
QI 2) a) Why is replacement of items required? Explain the theory of replacement with the help of example. [T]
b) Write any two applications of Games theory. Explain by giving probable strategies. [4]
c) Solve the following game. [T]
B

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