5. a.How can you solve an integer non linear programming problem?

(3)
b. Minimize f(X) = x: —X1X2 + 3x2! starting at X! = by the method of steepest
descent. (carry out only two iterations) (6)
6. a.What are the roles of exploratory and pattern moves in the Hook and Jeeves method? (3)
0. — Minimizef (ಸಿ) നോ —I startingat X, = 09 conjugate gradient
2
method. (6)
PART-C (Module V and VI)
„2 Consider the problem Minimize f(X) = (XI —l 224 (x2 — subject to 7

&= ->; + 11 -4 ऽ 0, ‏2ع‎ ಎ--2)28%-350
-1

Formulate the direction finding problem at X = as a linear programming problem 5 in
Zoutendijk's method. (6)

0. Minf(X) = X1? −− +10 subject to 4x1? 16 3x1+5X2SO

21, x2 0 with starting point X ಎ [-11] using cutting plane method. Complete one step

of the process.

(6)
8.8. Apply Kuhn -Tucker condition,to solve the following problem
∙ ⋅⋅ 1 2 2
Min f(X) = —2x1 — x2 subject _ ‏ديع‎ ٥,۲ 5316471202 20 (6)
b. Minimize Min f(X) = + subject 9२०0 = — 2 0, g2(X) = 2 0, byexterior penalty function

method. (6) = 2 2 0,

9. a.Determine whether the following optimization problem is convex, concave or neither type Min
f(X) ———4x1 + x; — 2x1x2 + , subjectto 2X1 +x2 ഉ 6, —4.12 SO, x,.X2>0 (6)

b. Solve the following Linear programming problem as a dynamic programming problem

Maximize 2 = Yr, +4x2 subject to the constraint2x] +x2 ऽ 40, 2X1 +5x2 ऽ 180,
-y, x2 20 (6)