đề thi tối ưu hóa

TrUong
D9i hqc Kinh
T€i
TP.
HeM
HQ
va ten:

Khoa Toan - Thong
ke
SBD :
______
~
___________
_
.
BE
THI MON TOI lJu HOA (QUY HOACH TUYEN TfNH)
Thoi gian lam bai: 75 phut
Khong
sa
d\mg tai
li~u
D~l
Cau
1.
Mot xi
nghi~p
d6 g6 dt! dinh san xua't
b~m,
ghe

va tu. Biet djnh muc tieu hao cae
K
K?
K kh'
l'
I?
h':>
h
b?
yeu to san xuat 1
am
ra
san. p
am
c 0 trong ang sau:
Yeu
to'
? K
san xuat
San phffm
Ban
Ghe
Tu
Lao dong
(ngaycong)
3,5 0,5
6
V6n san xua't
(tri~u
d6ng) 4,2 0,6 5,7

Ngoai ra biet gia
ban
cua
1 san phffm Ban, Ghe, Tu tuong
U'ng
Hi
5,4; 0,8; 7,2
(tri~u
d6ng) va xi
nghi~p
hi~n
co
sO'
lao dong
la
350 ngay cong,
sO'
v6n san xua't la 320
tri~u
d6ng.
sO'
ban va
sO'
ghe
phai tuan theo ti
l~
1
:6.
Gia
sa

m9i san phffm lam ra d8u
tieu
thl,l
du<jc
het.
Hay
l~p
mo hlnh bai toan tIm
ke
hO(,lch
san xua't sao cho t6ng
l<ji
nhu~n
t6i da. (Chi
l~p
mo hlnh, khong giai)
Cau2.
Cho bai toan quy
hO(,lch
tuyen
Hnh
sau day:
f=x,
+
2X2
~min
2xr +
X2
~
30

2Xl
+
6X2
~
30
XI
+
4X2
~
16
Xj,X2
~o
a) Giai bai toan tren
b~ng
phtidng
phap
ddn
hinh. TIm phuong an t6i u'u khac, neu
co.
b) Viet bai toan d6i ngftu va tIm
PATV cua
bfti
toan d6i ngftu
b~ng
cach
sa
dl,lng
djnh
ly
£>0

l~ch
bu yeu.
Cau3.
Giai bai toan
v~n
tai voi
s6li~u
sau day. TIm phuong an t6i
u'U
khac, neu co.
(a;) =(40, 50, 80)
(b)
=(40, 60, 100)
Chd
y:
Sinh vien
phdi
nqp
l{Ji
d~,
kern
VllO
bili thi.
Truong D?i hQc Kinh T e
TP.
HeM
HQ
va
KhDa
loT

Dan - Thong
ke
8BO:_________________________ _
BE
THI MON TOI
l1u
HOA (QUY
HO~CH
TUYEN TfNH)
Thai
gian
lam
bai: 75 phut
Kh6ng
sa
dl,mg
tili
Ii~u
D~2
Cilul.
Giai
bili toan
sau
bling phuong
phap
don hlnh.
'Om
phuong
an
t6i u'u khac, ne'u co.

[(x)
=
2x]
- 2x2
-4x3
- 4x4
-7
max
r
X
] -
2X
3-
X
4-
6
-3X3 +2X4
~4
X2
+X3
+
x4
4
1
xj
;:::
0,
j = 1,4
Diu
2.

Cho bili toan (P):
[(x)
=
3x]
+ 2x2 +
3x3
+ 5x4
-7
max
xl +X2 +
2X
3
+2x4
~
18
2x]
+2x2
+3x3
+4x4
=24
xl +2X2 +
2x
3 +3x4;::: 20
x j
;:::
0,
j = 1,4
L~p
bili
toan

d6i
ngau
(D) vil giai bili toan (D) bling
cach
sa
d\lng d!nh
19
DQ
l~ch
bu yeu, bie't rling
phuong
an
t6i u'u
cua
bai
toan
(P) lil x * = (4, 8, 0, 0).
Cilu
3.
Xet
bai toan
v~n
t~H
vdi
cae
s6li~u
sau:
(a/)=(45, 57, 28);
(b
j

)=(l8,
20, 25, 30, 37) va C=(Cij)3 5 xac d!nh
bOi:
[
~
~
::
:].
x
4 9 9 7 8
a) Giai bili
toan
v~n
tai tren.
b) Giai bili
toan
tren
vdi
dieu
ki~n
6 (3,
1)
Iii
6
c&m.
Ch6
y:
Sinh vien
phiii
nQP

It,li
d~,
kem vao
bai
thi.
TrUong
D~i
h9C
Kinh T
{f
TP.
HeM
Khoa
Toan
- Thong
ke
BE
THI
MON
TOl
VU HOA (QUY HOACH TUYEN TINH)
Thai
gian him bai: 75 phut
Khong sit
dl.mg
tai
li~u
D~3
Cau
1.

M('>t
hang
v~n
tai
c6
2
lo~i
xe
0 to
ch~y
tuy~n
Ba:c
- Nam:
Xe
lo~i
A
chd
dll(jc 45
ngllai
va
500
kg
hang
hoa, c6 chi phi moi
chuy~n
xe
la
24
tri~u
d6ng.

Xe
lo~i
B
chd
dll(jC
54 ngllai va 800 kg
hang
hoa,
c6 chi phi moi
chuy~n
xe
Ia 28
tri~u
d6ng.
Yeu
cffu phai
v~n
chuy~n
300
ngllai va 4 t:fn
hang
hoa
tlI'
Sai Gon ra
Ha
N(,>L
Hay
l~p
mo
hlnh

bai
toan
xac
dinh
so
0 to
c~n
sit
d\mg
sao
cho
tbng chi phi nh6
nh~t.
(Chll~p
mo hlnh,
khong
giai)
Cau2.
Cho bai toan quy
ho~ch
tuy~n
tinh sau day:
f=
Xl
+
4X2
~max
2xI
+
X2

~
84
XI
+
2X2
~
42
XI
+
4X2
~
70
XJ,X2
~O
a)
Giai
bai
toan tren bAng phu'dng phap ddn hlnh. TIm phlldng an toi
u'U
khac,
n~u
c6.
b)
Vi~t
bai toan doi ng§ u
va
tim PA
TV
cua
bai toan doi ng§u

bAng
each
sit d\mg dinh
19
B('>
l~ch
bu yeu.
Cau3.
Giai
bai
loan
v~n
tai voi
so
li~u
sau day.
TIm
phlldng
an
toi
u'U
khac,
neu
co.
3 8
6J
(aj)
= (30, 70, 100)
«Cij»
= 5 5 10

[
(b
j
)
=(30, 50, 80)
8 6
10
Chti
y:
Sinh vien phdi n9P i{Ii
ai,
kern
vao bai thi.
TrUong
D~i
h9C
Kinh Te
TP.
HeM
HQ
va
ten:
lC\\Y5(H'd
~\SJM~~
___ _
Khoa Toan - Th6ng
ke
saD:
'A:A
-~

BE
THI MON TOI
VU
HOA (QUY HOACH TUYEN TINH)
ThC1i
gian
lam
bai: 75 phut
Khong
sli'
dvng tai
li<$u
D~4
Ciiu
1.
Giai bai toan
sau
b:tng phuong
phap
don hlnh. TIm phuong
an
tai u'u khac,
neu
co.
f(x)
3x
1
+ 5x

2
+
4x}
)
min
2Xt+x2+2x3
6
4xI
+2x2
+3x3
22
-3x,
+2x2
-x3
~4
Xj20,j=1,3
Ciiu
2.
Cho bai toan (P):
f(x)
= -2XI +
x2
+ 4x3 + 4x4
~
min
x3
+x4
=7
-x2
-

3x
3
+2x4
~
6
-xI
+
2x
3
+x4
=8
Xj20,j=1,4
U~p
bai toan d5i
ng~u
(D)
va giai bai toan
(D)
b:tng
each
sli'
dl,mg
d~nh
19
DO
I<$ch
btl yeu, biet rhng phuong
an
tai u'u
eua

bai toan (P) la x * = (6,
0,
7, 0).
Ciiu
3.
Xet
bai toan
v~n
tai voi cae
s61i<$u
sau:
(a
i
)=(70, 80, 100);
(b
j
)=(60,60, 80, 100) va C =
(C
i
)3x4
xac dinh bdi:
IO
3 9 5
'\
4 5 6
12J'
r
\ 6 4 7 9
a) Giai bai toan
v~n

tai tren.
b) Giai bai to
an
tren voi
dieu
ki<$n
di€m thu
thu
3
nh~n
du hang.
Chti
y:
Sinh
vU~n
phdi
nQP
It;li
di.
kern
vao
bai
thi.