# Maximizr the profit function π=80x_2x^2-xy-3y^2+100y subject to x+Y=12 by using lagrange Method?

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- VamanLv 71 month ago
f(x)=80x_2x^2-xy-3y^2+100y subject to x+Y=12 by Lagrange method.

define

g(x,y)=80x-2x^2-xy-3y^2+100y +L( x+Y-12)

L is the Lagrange undetermined multiplier to be determined. Take partial derivative of g wrt x and y and equate them to 0.

wrt x gives

80-4x-y+L=0

wrt y gives

-x-6y+100+L=0

I am unable to solve it as we do not proper relationship. Is it x+y or xy=12?

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