168
Now if this is true allow u2 = u3 =//4 in Eq. (3.60) then
1
3
~Vl +~e4
> e~/4034/4
or
and using Eq. (3.62)
u~ + u4\6~.~
Now the general expression for geometric programming is
Using Eq. (3.61)
~ + ~ + u~ +’"Un _ ~} ~} ¯
Now in Eq. (3.65) if all Us are equal
3~+~2+63+...6n
~ 1 or
~ ~. = 1 for a minimum
So the equations are
Z 6iUi >~ I-I u~i
or
u i = 6 i Ui
S. ui>EXAMPLE 3.10. Minimize the following function [3.3,3.8]
g -- -- t- f12X2X3 + fl3XlX3 + fl4XlX2
Xl X2X3
Chapter 3
(3.63)
(3.64)
(3.65)
(3.66)
(3.67)
(3.68)
(3.69)
(3.70)
(3.71)
Now if this is true allow u2 = u3 =//4 in Eq. (3.60) then
1
3
~Vl +~e4
> e~/4034/4
or
and using Eq. (3.62)
u~ + u4\6~.~
Now the general expression for geometric programming is
Using Eq. (3.61)
~ + ~ + u~ +’"Un _ ~} ~} ¯
Now in Eq. (3.65) if all Us are equal
3~+~2+63+...6n
~ 1 or
~ ~. = 1 for a minimum
So the equations are
Z 6iUi >~ I-I u~i
or
u i = 6 i Ui
S. ui>EXAMPLE 3.10. Minimize the following function [3.3,3.8]
g -- -- t- f12X2X3 + fl3XlX3 + fl4XlX2
Xl X2X3
Chapter 3
(3.63)
(3.64)
(3.65)
(3.66)
(3.67)
(3.68)
(3.69)
(3.70)
(3.71)