172
Chapter 3
Next from 62
6 = 2/3 - -2~rh
Substitute for r Eq. (3.88)
Now check if V(6)=go by substituting for r and h
go = ~r 2 + 2grh
1 1/3 2
1
(3.89)
(3.90)
Yes! they are equal and a minimum has been found. Next check the constraint:
gr2h >_ 1
(3.91)
Substituting for r and h
[(1)1/312[(~) 1/3]
--~]
constraint is satisfied.
EXAMPLE 3.12.
From Example 3.7
Criterion function
Cost = 2~RZt-~ 3~zR
t
(3.92)
Functional constraints
Volume
4~R 3
-- > 57,750 in
3
(3.93)
3 -
Chapter 3
Next from 62
6 = 2/3 - -2~rh
Substitute for r Eq. (3.88)
Now check if V(6)=go by substituting for r and h
go = ~r 2 + 2grh
1 1/3 2
1
(3.89)
(3.90)
Yes! they are equal and a minimum has been found. Next check the constraint:
gr2h >_ 1
(3.91)
Substituting for r and h
[(1)1/312[(~) 1/3]
--~]
constraint is satisfied.
EXAMPLE 3.12.
From Example 3.7
Criterion function
Cost = 2~RZt-~ 3~zR
t
(3.92)
Functional constraints
Volume
4~R 3
-- > 57,750 in
3
(3.93)
3 -