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Question

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.

λ[gi(X') -bi]= 0, i =1,2,3...m

c.

gi (X ') ≤ bi , i = 1,2....m

d.

All of these

Answer: (b).λ[gi(X') -bi]= 0, i =1,2,3...m

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Q. 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...

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