Article From:https://www.cnblogs.com/yinwuxiao/p/9064290.html

The answer:

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

li * ki * (vivi)* 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

 

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