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thumb|300px|right|LaGrange Multipliers

I describe the contents of video to help readers' understanding.

We want to minimize C(x,y) = 6x^2 + 12y^2 subject to x+y=90. By Lagrange multiplier, we can write the Lagrange multiplier equation as

6x^2 + 12y^2 - \lambda(x+y-90).

Use the property of Lagrange multiplier that the partial derivatives of the above Lagrange multiplier equation should be equal to zero

F_x = 12x - \lambda = 0
F_y = 24y - \lambda = 0
F_\lambda = x + y - 90 = 0

From the first and the second equations, we will have x = \lambda/12 and y = \lambda/24. Putting these results to the third equation, we find

\lambda/12 + \lambda/24 - 90=0
\lambda/24 = 30
\lambda = 720,

which result that x = 30*24/12 = 60 and y = 30*12/12 = 30. Thus, the minimum of C(x,y) becomes 6(60)^2 + 12(30)^2 = 32400.

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