Part C
Minimizef(X) = —6X1?+ 1 10 + subject +x2?—-x: SO,
(2): ಖಂ +724, % —5<0, using penalty function method. (12 Marks)

Minimizef(X) = x/ + x: +x: + 40X1 + 20x2 subject to
80'): x, -50 20,
+X, 3೫) 10020, + x2 +x3 —15020. Determine whether the constraint

qualification and the Kuhn Tucker conditions are satisfied at the optimum point.
(12 Marks)

Minimize f(X) —4x2 subject + x3 = 12, g2(Y) :3x, +1 12 +x4 ಎ66, 20,i =
1,2,3,4 using Integer programming.

(12 Marks)