|
'
(c.
) L(
1
Step
D
,
x
µ
,
}
= +
)
Check
,
δ= (
2
htep
2
NDCQ
=
了
x
(
NDCO
,
FOc
.
0
,
o
Lx
.
=
2
》
=
2
(x
-
f (
+ (
Y
±
±
1
y
bot a (
Let
withr
set
,
(
+
xy
+
]
x
y
Y+
-
0
=
…
=☆
0
)
…
0
=
①
?
③
…
F
,
firax (
respect
2
2
x
y
-
U
a
;
,
G
x
=
*
+
x
0
-
3
.
=
>
[x 与 }
-
0
)
[x
λ
+
y 3
可
=
0
:
2
2
=
可 )
y
.
x
=
=
-
)
1
±
,
x
constraint
y )
2x +
u
y-
23
>③
,
⼲司
=
a,
(
µ
-
xtay
4
xiy
>
#
)
,
2
=
or
)
3
-
时
x
⾄x
Cbi )
2 x
=
y
+
moto n tohe
matisfied
Ts
(u
&
xy
+
,
is
)
Ly
ByD
=
'
(x
µ
.
y , xt 2 y
x+
wince
YL
.
Therefore
y
x
6
:
, aa
.
aa
)
to the
3
Maxirnrn
x
)
=
'
t
xy
t
Giy
be the Maxiomean valhe
parrarhetar
'
s
(
a
,
aa
az
the
of
)
-
,
optionication probleanr
fmax
( an
ar
,
13 )
afmcx l
)
, aislars tta
t
te a
)
-
=
Jey
-
(
=
r
>
fmax
,
0
1
,
)
1
.
lC )
.
6
≈
for
a
glo bal
莊
,
d
:
a
3
fxia
Hence
da
,
x
9
)
)
)
-
=
-
2
'
x +
a =
0
2
1
-
(
)
± ⽅,
1 . 1
(
-
)
3
)
=
=
:
驾
:
8
of
2
to
go
Tntinity
to
dugiee
f
so
,
,
and
x
=
fmaxla }
23
Ca
,
-
(
2
-
⾶
x
2 x
*
(
a
+
)
t
2x
2 a
)
+
a
f
Ja
*
oxx ia )
2
=
2a
些
a
=
3 ,
2, 8
=
Hence t
,
Ix1tends
Tff
⼲
=
2
polynonial
42
a +
t a
x
2
,
,
*
la
fmax
x
F 3
,
6
2
is a
value
⼩3
±
a
ts
weficiene
maximuurn
:
+
1
-
tutinity when
obtaiar
flx
tlx; a
,
negative
negaive
,
0
value
maximum
any
nith
(b )
6 (
-
.
the estimated
的
2
( 9
-
M
=
5a
⾶
t
8
+
a
x
2 x
*
(
a
3
+
8
*
:
x cc )
a
must
2
》
3
,
(c.
) ((
,
x
,µ )
y
xiy
50
:
^
(x
µ
-
+
Z
NDCQtfeJacobiarsmatrix
Lx
FOC
xi
25
=
'
1
Ly
>
.
(b
.
)
:
Theu
fi 16
Tleus
,
allocated
qx)
lef
L
let
=
=
to
y
to
79
;
G
l
1 hasfullrarrk
.
)
0
y
M
-
xry
-
80
-
)
0
=
=
h
.
0
=
…
①
…
0
…
- 80
=
0
23
X
=
16
=
Y
64M
:
25600
819200
geat possible
5
16
k
outfit
,
the 80 dollars bbhould
k
dollars to labor a n d 64 k
dllars to
be
eqiprmerrt
,
)
:
xey
-
a
^
-
be
la )
a
=
ows
xiy
fmax
espeot
,
(
千x
the la
yield
.
=
x
643
,
x+ y
glx
+4
X
)
^
( xey
-
可
toll
as
50
=
>
③
lo
=
Lie
① & ②
is
80
satisfied
NDCOis
的
-
,
p(
the
x+y
-
a
maximum
)
value
ofthe
opimicationProblem
vith
,
tmax f
h
s
+
8
max
7
ta
s
⼦
=
-
.
lurax
25600
=
za
[(
Heuce
Theretore
⼭
the estimated
,
分 44800
Ts
fmax C 79
vill brave
we
-
19200
change
)
≈
819200
6
,
64 2500 ]
,
25600
-
(
79
-
80
)
844800
=
maxinunoutput
in
25600
=
[a )
Case I
:
Al )
+
2
All the
'
3
Heuce
:
.
2
x
two
(
E
ul
possible
=
not
4
Matrices
y
the
0
=
on
=
4
Czx
are
到
=
0
0
)
cre
Matrices
Lo 3 )
'
,
binding
IDCQ isbatintied
4y )
are
,
is
(
o
.
0
)
C
-
1
0
.
}
s
.
[
o
)
1
-
.
However Cx
,
,
y )
al offoiam
=
ase
{
0
o
,
]
full rank
binding
(比 ) .「
。
.
,
corrsfaaiut set
onstraints
Jawbian
possible
By
applying
Case
the
f
Ts
Cane
binding
coustraint is
one
比
2 .]
1
)
ranklofthem
have tull
respectively
imposnible
L
(b )
.
y
x+
=
FOC
λ (
-
Lx
:
=
Ly
=
x
+ 2z
|
-
1
4 λ,
-
λ [
'
x
2
+
2
x
X
≥
Y
0
,
if
CC .)
x1
Thus
0
=
obtain Cx
ve
xa2 y=
:
f
For
y
Thus
λ
2
-
lof furax
( .
,
.
0
,
f
(d )
.
Let
Ix Y
,
2
fmax
(b
to
zepeof
fomaxlo 9
b.
I 1
11
.
,
.
b
,
λλa
,
,
2.
(2
λ
3
}
1
,
.
,
y
,
0
=
1 ]
,
>
x
2
=
1
,
t
,
0
,
=
x
2
⼦
2
xtzy ÷
6
)
0
,
=
)
≈fmax (
]
2
1
,
t
,
,
0
3
0
,
{
0
,
.
,
0
6
到
0
}
0
-
+λ ,
)
2
:
(
.
.
5
9
-
6
)
xalo
.
2
o
-
]
975
]
the problem vith
) bethemaximum valueof
4
啊 b4 b 5
,
.
1
,
,
,
597
fmax
≈
-
where ( x
(
=
f
3
. bn , b , b 5
ba
b
2
,
:
=
(
=
+λ
where
X
0
01
,
2
.
3
,
0
0
1
:
0
x
0
=
λ2 λ s )
X
9
-
2
3
市
=
1
( xiy , 1 .
5
(
=
o
λ
.
*
λ
=
y )
-
0
=
as
λs )
"
0
=
λ2
.
and
=λ>
2
,
frax
khow
l
1
-
>
obtain
we
we
⼆,
x
.
=
a
2
0
1
=
λ
0
λ
, x
(
6
,
y
3
0
20
Xa
s
3
=
x
cnd yf
∴
.
6
,
λ
-
0
三
xa
s
)
=
)
=
y
2
+
x
-
=
a
+λ 3
=
λ 等
2
Y
λ2 (
-
+λ
x
6
λλ x
6 )
-
,
λ
-
y
=
λλ 2 , n
λ
)
=
(
z
2 λ
.
1
,
(
1 , . 1
1
Y[
]
.
,
.
2
,
6
]
11 - 13
0
,
0
txlo .
+λ
9
1
-
1
)
:
+
3
y {
0
,
11
2
13
-
to
,
xixI
-
1
-
005
t
1
.
0
-
,
1
25
}
=
3 1
,