Re: Inequality with max I want to understand

Hi,

I was reading a paper and hit an inequality I have
never seen before:

(a + b) / (c + d) <= max (a/c, b/d)

In the paper I have the additional constraints that c
0, d > 0, a >=
0, b >= 0.
I am interested in where this comes from and other
examples. If there
are
books or other resources that contain stuff similar
to this I would
like to know.
I have no idea how I might search for something like
this online for
example.
I haven't sat down yet for an extended period to try
and prove this.
I don't really have an idea of how to try and tackle
it either.
Mathematica can find counter examples with negative
variables but not
with the additional constraints.

Thanks.
Neill.

Suppose not, and let t := d/c > 0.
Then we have:
0 <= a + a*t < a + b and
0 <= b + b/t < a + b, hence

0 <= a*t < b, and 0 <= b/t < a. Now, multiply these...
.

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