9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
Chapt
er2AnI
ntr
oduc
tio
ntoLi
nea
rPr
b ogr
a
mming
Le
arni
ngOb
jec
tiv
es
1. Obt
ainanover
viewoft
heki
ndsof
probl
emsl
i
n ea
rpr
ogrammi
n ghas
beenus
edt
o s
olve.
2. Le
arnhowt
o de
v el
o pl
ine
arprogrammingmodel
sfors
impl
epr
oblems.
3. Be
abl
etoi
d e
n t
i
fyt
h e
spe
cial
fea
tur
esof
amode
lt
h at
m a
k e
it
ali
n e
arpr
o gr
ammi
n gmodel
.
4. Le
arnhowt
o s
o l
v e
twova
ri
abl
el
ine
arpr
o gr
ammi
n gmode
ls
b yt
h e
g r
aphi
cal
sol
u t
i
o npr
o c
edur
e.
5. Unde
rst
andt
h e
impor
t
a nc
eof
ext
reme
p oi
n t
si
n obt
aini
n gt
h e
o pt
i
m a
ls
o l
u t
i
o n.
6. Knowt
h e
u s
eandi
n t
erpr
eta
ti
o nof
sl
acka
n ds
u r
p l
u s
v a
ri
abl
es.
7. Be
abl
etoi
n t
erpr
ethe
comput
ers
o l
u t
i
o nof
ali
n e
arpr
o gr
ammi
n gpr
o bl
em.
8. Under
st
a ndhow al
t
e r
n at
i
v e
o pti
m a
ls
o l
u t
i
o ns
,
inf
eas
ibi
l
i
tya
n dunbounde
d ne
ssc
anoc
cur
i
n l
i
n e
arb
b programm ingpro blem s.
9. Unde
rst
andt
h e
fol
l
o wi
n gt
erms
:
problemb form u l
ati
o n f
e asi
b l
ere gio n
co n str
a i
n t
fu ncti
o n sl
a ck va ri
a b l
e
o bj
e c t
i
v efu ncti
o n st
an da r
d form
so l
u ti
o n r
e du n da n t
c on st
rai
n t
o pti
m a l
so lut
io n extrem e poi nt
n on n e ga t
i
v i
tyc on st
rai
n t
s su r
p l
u sv a r
iab l
e
ma the matical m odel al
ternati
v eo p t
im al
so l
u t
i
o ns
l
in ea rp ro g r
a m i
n feasi
b il
i
ty
l
ine a r
fu n ct
ion s
unbounded
b f
eas
ibl
esol
u t
i
o n
2-1
about:blank 1/46
,9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
Chapter2
Sol
u t
ions
:
1. a
,b,
ande
,ar
eac
cept
abl
eli
n e
arpr
o gr
ammi
n gr
ela
ti
o ns
h i
p s
.
2
cisnotacceptablebecauseof-
b b 2B
disnotacceptablebecauseof3b b A
f
isnotac
ceptabl
e bec
aus
e of1AB
c,
d,a
ndf
coul
dnot
bef
oundi
n al
i
nea
rprogrammi
n gmodel
beca
uset
h eyha
vet
h e
above
nonl
i
nea
rb b t
erms.
2. a.
b.
c.
3. a.
2-2
about:blank 2/46
,9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
AnI
n t
r
oduc
ti
ont
oLi
n e
arPr
o gr
ammi
n g
b.
c.
B
Po int
s b o nl
in
eareon l
y b fea
s
ibl
esol
u t
i
o ns
(
0 ,
2 0)
A
0 (
4 0,
0 )
4. a.
b.
2-3
about:blank 3/46
, 9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
Chapter2
c.
5.
6. 7A+10B=420islabeled(a)
2-4
about:blank 4/46
6
Chapt
er2AnI
ntr
oduc
tio
ntoLi
nea
rPr
b ogr
a
mming
Le
arni
ngOb
jec
tiv
es
1. Obt
ainanover
viewoft
heki
ndsof
probl
emsl
i
n ea
rpr
ogrammi
n ghas
beenus
edt
o s
olve.
2. Le
arnhowt
o de
v el
o pl
ine
arprogrammingmodel
sfors
impl
epr
oblems.
3. Be
abl
etoi
d e
n t
i
fyt
h e
spe
cial
fea
tur
esof
amode
lt
h at
m a
k e
it
ali
n e
arpr
o gr
ammi
n gmodel
.
4. Le
arnhowt
o s
o l
v e
twova
ri
abl
el
ine
arpr
o gr
ammi
n gmode
ls
b yt
h e
g r
aphi
cal
sol
u t
i
o npr
o c
edur
e.
5. Unde
rst
andt
h e
impor
t
a nc
eof
ext
reme
p oi
n t
si
n obt
aini
n gt
h e
o pt
i
m a
ls
o l
u t
i
o n.
6. Knowt
h e
u s
eandi
n t
erpr
eta
ti
o nof
sl
acka
n ds
u r
p l
u s
v a
ri
abl
es.
7. Be
abl
etoi
n t
erpr
ethe
comput
ers
o l
u t
i
o nof
ali
n e
arpr
o gr
ammi
n gpr
o bl
em.
8. Under
st
a ndhow al
t
e r
n at
i
v e
o pti
m a
ls
o l
u t
i
o ns
,
inf
eas
ibi
l
i
tya
n dunbounde
d ne
ssc
anoc
cur
i
n l
i
n e
arb
b programm ingpro blem s.
9. Unde
rst
andt
h e
fol
l
o wi
n gt
erms
:
problemb form u l
ati
o n f
e asi
b l
ere gio n
co n str
a i
n t
fu ncti
o n sl
a ck va ri
a b l
e
o bj
e c t
i
v efu ncti
o n st
an da r
d form
so l
u ti
o n r
e du n da n t
c on st
rai
n t
o pti
m a l
so lut
io n extrem e poi nt
n on n e ga t
i
v i
tyc on st
rai
n t
s su r
p l
u sv a r
iab l
e
ma the matical m odel al
ternati
v eo p t
im al
so l
u t
i
o ns
l
in ea rp ro g r
a m i
n feasi
b il
i
ty
l
ine a r
fu n ct
ion s
unbounded
b f
eas
ibl
esol
u t
i
o n
2-1
about:blank 1/46
,9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
Chapter2
Sol
u t
ions
:
1. a
,b,
ande
,ar
eac
cept
abl
eli
n e
arpr
o gr
ammi
n gr
ela
ti
o ns
h i
p s
.
2
cisnotacceptablebecauseof-
b b 2B
disnotacceptablebecauseof3b b A
f
isnotac
ceptabl
e bec
aus
e of1AB
c,
d,a
ndf
coul
dnot
bef
oundi
n al
i
nea
rprogrammi
n gmodel
beca
uset
h eyha
vet
h e
above
nonl
i
nea
rb b t
erms.
2. a.
b.
c.
3. a.
2-2
about:blank 2/46
,9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
AnI
n t
r
oduc
ti
ont
oLi
n e
arPr
o gr
ammi
n g
b.
c.
B
Po int
s b o nl
in
eareon l
y b fea
s
ibl
esol
u t
i
o ns
(
0 ,
2 0)
A
0 (
4 0,
0 )
4. a.
b.
2-3
about:blank 3/46
, 9/14/23,b11:51bAM Chapterb02bSolnbUpdatedb11121
6
Chapter2
c.
5.
6. 7A+10B=420islabeled(a)
2-4
about:blank 4/46
