Subject to +2x2 54, 2Xi +x2 '6, »q,X2 20 and are integers.

a. Write the dual of the following LPP: (4)
Maximize Z = — X2 +3X3

Subject to +X2 SIC, 2K, —X3 E2, 2X1 —2X2 +3X3 56, X),X2,X3 20.
0. Solve the mixed integer programming problem graphically: (5)
Maximize 7 = ‏اا‎ 2
Subject to 324 +2x2 55, 22 < २, x,,.X2 20 and is an integer.

PART C

a.Minimize f(x,y) =2x 2+۷ 2+2xy—Y+x by using Fletcher-Reeves method. Take (6) (0,0) as
the initial point.

b. By applying steepest descent method, Minimize f(x,y) = 4x 2 —4xy +2y 2 with initial (6)
point (2,3). Use two iterations.

a. Describe Powell's method for solving the unconstrained minimization of a function of (6)
two variables.

b. Use dynamic programming to solve the following problem: (6) Minimize +۷2 +۷3
Subject to +2 215, 20.

a. Solve the following nonlinear programming problem using Kuhn-Tucker conditions:
(6)

Maximize 2 2 3x,2+14xp<2 —BC

Subject 30 +6x2 ऽ 72, x,,xa 20.

b. Give the necessary conditions and the modified linear programming problem (6)
associated with the QPP: Maximize

(1, 2) =8X, 410x2 2012-3
Subject to 3Xl+2X2 56, x, 20, x2 20.