Need help with Lagrange multiplier question?

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1 Answer
Apr 15, 2018

See below.

Explanation:

L(x,y,lambda) = 5x^2+6y^2-xy + lambda(x+2y-24)

grad L = ((10x-y+lambda),(-x+12y+2lambda),(x+2y-24))=((0),(0),(0))

Now solving for x,y,lambda

x=6, y = 9, lambda =-51 ----(*)

The qualification is done over f @ g or

f@g = 7x^2-84x+864

hence x = 6, y = 9 as determined in (*) is a local minimum.