Optimum Design
171
This obtains a dual objective function
V(6) = gogi or
or
V(6) --~ go(x) for a minimum
Now V(6) is a minimum if the powers on r and h are 0 or orthogonality
constants for Eq. (3.82)
261+62-2611 =0
(3.83)
62-61~ =0
Also Eq. (3.67)
6~ + 62 = 1
(3.84)
for the constraint, a 2nd normality constraint
61 = ~,,
(3.85)
A solution gives
61 = I/3 62 = 2/3 6’, = 2/3 g, = 2/3
(3.86)
Answers are obtained when V(6) is evaluated r °, h ° are 1
17: I/3 2re 2/.3 I
2/3
213
__
Now from 6~
1
Ul
~r 2
6~ 3 V(6)
2/~
r2=(~)2/3
r=(~) 1/3
(3.87)
(3.88)