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2009 IberoAmerican Olympiad For University Students
3
Find the maximum of a product - OIMU 2009 Problem 3
Find the maximum of a product - OIMU 2009 Problem 3
Source:
May 23, 2010
inequalities proposed
inequalities
Problem Statement
Let
a
,
b
,
c
,
d
,
e
∈
R
+
a, b, c, d, e \in \mathbb{R}^+
a
,
b
,
c
,
d
,
e
∈
R
+
and
f
:
{
(
x
,
y
)
∈
(
R
+
)
2
∣
c
−
d
x
−
e
y
>
0
}
→
R
+
f:\{(x, y) \in (\mathbb{R}^+)^2|c-dx-ey > 0\}\to \mathbb{R}^+
f
:
{(
x
,
y
)
∈
(
R
+
)
2
∣
c
−
d
x
−
ey
>
0
}
→
R
+
be given by
f
(
x
,
y
)
=
(
a
x
)
(
b
y
)
(
c
−
d
x
−
e
y
)
f(x, y) = (ax)(by)(c- dx- ey)
f
(
x
,
y
)
=
(
a
x
)
(
b
y
)
(
c
−
d
x
−
ey
)
. Find the maximum value of
f
f
f
.
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