x1.x2Q

5. a. Write the dual of the following LPP(4 marks)

Maximize f = 4x1 + 2xz

Subject tOX | — 2X2 2 ; X1+2X2=8; 2ല X211;
212 0 ; X2 unrestricted. b.

Solve by Graphical Method(S marks)

Maximize 2 71 + 3x2

Subject to ۸1+ 2X2 2 3 ; + ೫2 4; Xi
12 2 0 + integers.
6. Solve the Integer Programming Problemby Cutting plane method (9 marks)

Maximize Z = 2x + 3y
Subject to 2x+2y< 7: > 2:35 2;
x, y20;x and $ integers.
PART ೮ (MODULE V & VI)

7. a. Minimize f = 20 + 2x2 from the starting point (1,1) ,using Steepest
Descent Method. (Two Iterations) (6 marks)

b.Write the Kuhn-Tucker conditions for Minimize f = x} +
2x; + 3x3 ; subject to —— 2x3 12 ; x, + 2x2 — 3x3 8.(6 marks)

8. 2. Write down the iterative procedure of Fletcher Reeves Method? (6 marks) b. Use

Hooke Jeeves method to solve

Minimize f(X) = 3x; + x; — 12x1 — 8x2; withX= = and − 05.

9. a. Write the necessary conditions for the optimal solution of the QPP(6 marks)

Min f(x) = 3X1 + X2 + 2XIX2 + XI + 657 + 2 subject to 2x1
+ 3x2 2 4; 21, 2४2 20.

b. Determine 111, ti2.u3 so as to maximize uruzu3 subject to ut + uz + = 10 and 112,

O. (6 marks)