I find Lagrange multiplier is really a good thing.
I wouldn’t say that I used this thing for the most purpose in mathematics competition.
Since I’m not very good at hitting that symbol, I use Li to represent lanmuda in normal partial derivatives.
This problem can be obtained in a simple way
2 li * ki * (vi−vi′)* vi^2=1
And then once the Li is determined
We will find that the three function is a single peak of two points (because the restriction is monotonous).
And then we’ll find out
Our goal equation: sigma (ki* (V-VI) ^2*si) increases with the increase of VI, while VI decreases with the increase of Li.
So the relationship between Li and W is also monotonous
So we can also get two points