Download AKTU B-Tech 6th Sem 2015-2016 NME 011 Engineering Optimization Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 6th Semester (Sixth Semester) 2015-2016 NME 011 Engineering Optimization Question Paper

Printed Pages: 4 NME-011
(Following Paper ID and Roll No. to be ?lled in your
Answer Books)
RollNoillIIlllll
B.TECH.
Theory Examination (Semester-VI) 2015-16
ENGINEERIN G OPTIMIZATI ON
Time : 3 Hours Max. Marks : 100
Section-A
1. Attemp all question. All questions carry equal mark.
Write answer of each question in short. (2XI0=20)
(a) Write the linear programming problem- in standard
form.
(b) What is a Pivot operation?
(c) State the Kuhn-Tucker conditions.
(d) What is the difference between Newton and
Quasi?Newton method?
(e) What is the limitation of the linear extended penalty
function?
(0 How is the direction-?nding problem solved in
Zoutendijk's method?
(1) P.T.O.
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(g) Why is Rosenbrock method called the method of ro-
tating coordinates?
(h) What is Univariate method?
(i) What is normality condition in a geometn'c program-
ming problem?
(j) De?ne a complementary geometric programming
problem.
Section-B
Attempt any ?ve questions from this section.
(10x5=50) I
(a) Maximize f = xl+2x2+x3
Subject to 2xl+x2?x332
?2x1+x2?5x32?6
xl+2x2+xss6
xiz 0, i = 1, 2, 3
Using simplex method.
(b) Minimize f (Xv x2) = (x1?1)2 ? x22
Subject to g1 (x1, x2) = x13 ? 2x230
g1 (x1, x2) = x13 + 2x250
(2)
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(C)
(d)
(e)
(0
Determine whether the constraint quali?cation and
Kuhn-Tucker conditions are satis?ed at the optimum
point.
Find the dimensions of a box of largest volume that
can be inscribed in a sphere of unit radius.
Minimize f (x1, x2) = x1 ? x2
Subject to g(xl, x2) = 3x12 ? 2x1x2+x22?ISO
Using the cutting plane method. Take the conver-
gence limit in step 5 as = 0.02.
Derive the expression for solution of an Uncon-
strained Geometric Programming program using
Differential Calculus.
In a certain reservoir pump installation, the ?rst cost
of the pipe is given by (100 D+ 50 D2), where D is
the diameter of the pipe in cm. The cost of the res-
ervoir decreases with an increase in the quantity of
?uid handled and is given by 20/Q, where Q is the
rate at which the ?uid is handled (cubic meters per
second). The pumping cost is given by (300Q2 /D$).
Find the optimal size of the pipe and the amount of
?uid handled for minimum overall cost.
(3) P.T.O.
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(g) Minimize f (x1 ,x2) = xl-x2 +2x12+2x1x2+x22 starting
from the point x]: {3 using CAUCHY METHOD.
(h) What are the Rank 1 and Rank 2 Updates in QUASI-
NEWTON Methods?
Section-C
Attempt any two questions from this section. (15X2=30)
3.
Explain the Exterior Penalty Function Method with suitable
example.
Solve the following LP problem using the braych and bound
method:
Maximize f = 3x1+4x2
Subject to 7xl+l 1x2 S 88
Design a helical spring for minimum weight subject to a
constraint on the shear (1) induced in the spring under a
compressive load P.
(4)
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