Optimisation problem

[Guest]

Divide 30 into 2 parts so that the sum of the squares of the parts is a minimum.

thanks in advance

 

[jacket81]

problem

Letting x, y be parts, then x+y=30, and you want to find minimum of x^2+y^2.
SO, x=30-y. Substittue that in x^2+y^2, giving you (30-y)^2+y^2, or 900-60y+y^2+y^2 = 900-60y+2y^2.
Differinate that, giving you -60+4y and set to 0. SO, you have -60+4y=0.
And, I know you can find answer from there.