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International Contests
IMO Shortlist
1981 IMO Shortlist
3
7 variables inequality
7 variables inequality
Source:
September 15, 2010
maximization
optimization
algebra
Inequality
IMO Shortlist
Problem Statement
Find the minimum value of
max
(
a
+
b
+
c
,
b
+
c
+
d
,
c
+
d
+
e
,
d
+
e
+
f
,
e
+
f
+
g
)
\max(a + b + c, b + c + d, c + d + e, d + e + f, e + f + g)
max
(
a
+
b
+
c
,
b
+
c
+
d
,
c
+
d
+
e
,
d
+
e
+
f
,
e
+
f
+
g
)
subject to the constraints(i)
a
,
b
,
c
,
d
,
e
,
f
,
g
≥
0
,
a, b, c, d, e, f, g \geq 0,
a
,
b
,
c
,
d
,
e
,
f
,
g
≥
0
,
(ii)
a
+
b
+
c
+
d
+
e
+
f
+
g
=
1.
a + b + c + d + e + f + g = 1.
a
+
b
+
c
+
d
+
e
+
f
+
g
=
1.
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