1. Find and solve the first order conditions associated to the problem: Minimize xy subject to x2 + 4y2 = 1.
Need to solve this using the Lagrangian
I have done the following
U(x,y) - λ(x^2+4y^2-1)
(1) dL/dx = y-λ2x=0
(2) dL/dy = x- λ8y=0
(3) dL/dλ = -(x^2 + 4y^2-1) = 0
(dL/dx)/(dL/dy)= (y- λ2x)/(x- λ8y)
x/y=8y/2x
(x/y)2x=8y
2x^2/y=8y
2x^2/8y=y
I just wanted to make sure these steps were right before i substituted it in to the original formula.
Thanks
Need to solve this using the Lagrangian
I have done the following
U(x,y) - λ(x^2+4y^2-1)
(1) dL/dx = y-λ2x=0
(2) dL/dy = x- λ8y=0
(3) dL/dλ = -(x^2 + 4y^2-1) = 0
(dL/dx)/(dL/dy)= (y- λ2x)/(x- λ8y)
x/y=8y/2x
(x/y)2x=8y
2x^2/y=8y
2x^2/8y=y
I just wanted to make sure these steps were right before i substituted it in to the original formula.
Thanks
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