RTU 2016 Question Paper Semester IV Civil Engineering Optimization Techniques

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RollNo. Total No of Pages: I
4E2039
B.Tech. IY-Sem (Back) Examl June-July 2016
Civil Engineering
4C86.2(O) Optim ization Techniques

Time: 3 Hours Maximum Marks: 80
Min. Passing Marks (Main & Back): 26
Min. Passing Marks (OId Back): 24
I nstructions to Candidate s : -

Attempt any ftve questions, selecting one questi.on from each unit. All
Questions carry equal marks. Schematic diagrams must be shown
wherever necessary. Any data you feel missing suitably be assumed and
stated clearly.
Units of quantities used,/ calculated must be stated clearly.

Use of following supporting material is permitted during examination.

(M entioned in form No.205 )

UNIT.I
Q.1 (a) What do you mean by optimization techniques? Write its applications in the field
of engineering. t8l
(b) A company produces two types of leather belts A and B. The respective profits
are Rs.10 and Rs.5 per belt. The supply of raw material is sufficient for making

850 belts per day. For A, a special type of buckle is required and 500 are
available per day. There are 700 buckles available for belt B per day. Belt A
requires twice as much time as that required for belt B. The company can
produce 500 belts if all of them were of type A. Formulate a model for the above
problem. t8l

14F,203e1 Page 1 of4 [e0o]

OR

Q.1 (a) Prove that the semi vertical angle of the cone of maximum value and of given
slant height is tan-1J2 . t81

(b) Find the dimensions of a box of largest volume that can be inscribed in a sphere
of unit radius. t8l

UNIT.II
Q.2 (a) Solve the following LPP by simplex method- t8l
Max.z= 3x1 +5x2+4x3
s.t. 2x1+3x2<8
2x2+ 5x3 < 10
3x1 + 2x2+ 44315

and Xl, X2, x3 2 0
(b) Solve the dual of the following LPP by simplex method- t8l
Min.z= 2x1+9x2+x3
s.t. . xr +4x2+2425
3x1 + x2+ 2424
and X1rX2, X3 2 0

OR

Q.2 (a) Solve the following LPP by revised simplex method- t8l
Max.z= x1*2x2
s.t. X1*x2(l
x1 I 2x23 5
3xr + xz(6
and X1, x2 )0
(b) Use Big. M - Methgd to solve. t8l
Max. z = 3x1+2x2+x3
s.t. - 3x1 + 4x2+ xz=7
- 3x1 + 2x2+ 24- 8

Xl, X2, Xf ) 0
148203el Page2 of4 [eoo]

Q.3 (a) Solve the transportation problem for which the cost, availabilities and
destinations are given below. tSl
W1 W2 W3 Wa Supply
F1 2351 7
F2 7346 9
F3 4t72 18
Demand58714
O) Solve the following assignment problem t8l

I II m IV V
A 1 J 2 -J 6
B 2 4 J I 5
a
C 5 6 J 4 6
D J I 4 2 2
E 1 5 6 5 4

OR

Q.3 (a) Solve the following unbalanced transportation problem: t8l
X Y Z Availability
A 736 5 I

B 468 10
C 584 7

\- D 843 a
J

Demands 5810
(b) Solve the following assignment problem t8l
\ Machines
Jobi\ D1 D2 D3

01 20 27 30
02 10 18 t6
0. t4 t6 t2

l4E203el Page 3 of4 [eo0]

UNIT.IV
Q.4 (a) Minimize f = 2xt2 * xz2,from the starting O"a, lllrsing univariate method or
other direct search method. t8l

r r/ x,z')= 1(*, + l)' + x,
(b) Minimize f (x,, tSl
3'

s.t. g,(x,,xr)=1-x, S0
gr(x,, xr)= -x, ( o
.
OR
Q.4 (a) What are various methods employed in solving the non- linear optimization
problems. Give a brief of any one method. t8l
(b) Use descent method to minimize f1 (x1, xz) = xr - xz * 2xl + 2x1x2 + x22, by
taking the starting polnt x, =[l] t8l
'
(.0/

UNIT.V
Q.5 (a) Use dynamic programming to solve: t8l
MinZ= uf + u] + u]
s.t. u1 *u2+u3>15
Ul, U2, Uf > 0
(tl Define "Bellman's principle of optimality" what are characteristics of dynamic
programming problem. Write the engineering applications of dynamic
progralrurung. t8l

Q.5 (a) Use dynamic programminr,o ror#
Mi1 Z= yl+yzz+yz2
s.t. Yr+YztYl=10
Yt,Yz, Y: 2 0
(b) Solve the problem by dynamic programming technique. t8l
NItnZ= u1u2 u3
s.t. u1+u2+u3*5
Ul, U2, Uf ) 0

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