Q2,paper 3,D13. Given the problem to maximize f(x), X = (x1, x2,......xn) subject to m number of inequality constraints. gi(x) ≤bi, i = 1, 2......m including the non-negativity constraints x≥0. Which of the following conditions is a Kuhn-Tucker necessary condition for a local maxima at x’?

(A) ∂L(X’, λ’, S’) /∂xj= 0,                          j = 1, 2....m

(B) λi[gi(X’) – bi]= 0,                                 i = 1, 2 ....m

(C) gi(X’) ≤bi,   i = 1, 2 ....m

(D) All of these.

Answer D.