(2 Pages)

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER M.TECH DEGREE EXAWNATION,MAY 2017

Mechanical Engineering
(Machine Design)

01ME6122: Optimization Technique for Engineering

Max. Marks: 60 Duration: 3 Hours Answer two questions from each part. ۸

[~

. Find the dimensions of a box of largest volume that can be inscribed in a sphere of unit
radius.(9 Marks)

2. a) Find the second order Taylor series approximation of the function
८५००) = 2 +, (5 Marks)
b) Determine whether the following functions are concave or convex. 7)7(%)- 4x1
43024 5X3 437/2205 + ൭0 — 2X2 +154) S(X) -6െ.
(4 Marks)

3. a) Mention any five applications of optimization in the field of mechanical engineering.
(3 Marks)
b) What are objective function contours? (3 Marks) c) Under what conditions can a

polynomial in 'n' variables are called a Posynomial?

(3 Marks)
Part B
0.75
4. Minimize f(x) = 0.65— —0.65xtan -1 (—) in the interval 10, 3] by the Fibonacci
x
method conducting six experiments. (9 Marks)
2
5. Minimize / (225(४ - 2 റ 2) from the starting point X/=-2.-2/using
Fletcher - Reeves method. (9 Marks)

6. Find the optimal control 'u' that makes the functional J = f (x 2 -eu2)dt Stationary with
x=uand The value of 'x' is not specified at [=]. (9 Marks)

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