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Consider the minimisation and maximisation of the objective function f : R2 + R given by f(x,y) = (1 - 1)2 + y2 + 3 on the fe

(a) Write down a Lagrangian function L(x, y, 1) whose only stationary point (x*, y*, \*) corre- sponds to the point of tangen

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Answer #1

Answed. Given data: - f(x+y) - (x-1)2 + y2 +3 Interior of the right- angled txangle whose veotices are Points (002, (20) and3) L(X,Y,») = (x-1)-1.42+3+-) (4x+3y-12) Diffidentiate with respect to x on both sides UL JX 2(x-1) +47 Sn: ladly 山西 = 29+3Now f(x,y)= + (575, 2465 245) substitute Clubiono we get, - (-1)+24,73 +(5445,24,5) =139 /₂5 SO This is the is the minimum va

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