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Weighted open-box minimization
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Mathematics
Area of mathematics
Mathematical optimization
Lagrange multiplier
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For a topless rectangular box with dimensions
x
,
y
,
z
, volume
V
, and weighted face cost
A
=
a
x
y
+
b
x
z
+
cyz
,
(10)
an interior optimum equalizes the three terms:
a
x
y
=
b
x
z
=
cyz
.
(11)
The same result and global minimality follow from the arithmetic-geometric mean inequality.
Ancestors
(5)
Lagrange multiplier
Mathematical optimization
Area of mathematics
Mathematics
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(1)
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