Write the KKT necessary conditions for the following problems:

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Write the KKT necessary conditions for the following problems:
(a)
max r – a + rja
s.t.
x1 + x+ x3 = 5
5a – a3 – x3 2 2
X1, X2, X3 2 0
(b)
min a+ x+5x1x2x3
s.t.
xỉ - 3 + a< 10
a+ a+ 4x > 20
(c)
min af + a + a3
s.t.
2.x1 +x2 < 5
x1 + x3 < 2
xị > 1
x2 > 2
X3 >0
Transcribed Image Text:Write the KKT necessary conditions for the following problems: (a) max r – a + rja s.t. x1 + x+ x3 = 5 5a – a3 – x3 2 2 X1, X2, X3 2 0 (b) min a+ x+5x1x2x3 s.t. xỉ - 3 + a< 10 a+ a+ 4x > 20 (c) min af + a + a3 s.t. 2.x1 +x2 < 5 x1 + x3 < 2 xị > 1 x2 > 2 X3 >0
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