1. 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 dmg 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' ? Ksan 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.

2. Truong D?i hQc Kinh T eTP. HeM HQ va
KhDa loTDan -Thong ke 8BO:_________________________ _
BE THI MON TOI l1u HOA (QUY HO~CHTUYEN 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 rX] -2X3-X4-6 -3X3 +2X4 ~4 X2 +X3 + x4 41 xj ;::: 0, j = 1,4
Diu 2.
Cho bili toan (P):
[(x) = 3x] + 2x2 + 3x3 + 5x4 -7 max
xl +X2 + 2X3+2x4 ~ 18
2x] +2x2 +3x3 +4x4 =24
xl +2X2 + 2x3 +3x4;::: 20
x j ;::: 0, j = 1,4
L~p bili toan d6i ngau (D) vil giai bili toan (D) bling cach sa dlng 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); (bj )=(l8, 20, 25, 30, 37) va C=(Cij)35 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.

3. 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 Achd 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 dmg 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 PATV cua bai toan doi ng§u bAng each sit dmg 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
[ (bj) =(30, 50, 80)
8 6 10
Chti y: Sinh vien phdi n9P i{Ii ai, kern vao bai thi.

4. TrUong D~i h9C Kinh Te TP. HeM HQ va ten: lCY5(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<$u
D~4
Ciiu 1.
Giai bai toan sau b:tng phuong phap don hlnh. TIm phuong an tai u'u khac, neu co.
f(x) 3x1 + 5x2 + 4x} --) min 2Xt+x2+2x3 6 4xI +2x2 +3x3 22 -3x, +2x2 -x3 ~4
Xj20,j=1,3
Ciiu 2.
Cho bai toan (P):
f(x) = -2XI + x2 + 4x3 + 4x4 ~min
x3 +x4 =7 -x2 -3x3+2x4 ~ 6 -xI + 2x3+x4 =8 Xj20,j=1,4
U~p bai toan d5i ng~u (D) va giai bai toan (D) b:tng each sli' dl,mg d~nh 19 DO I<$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<$u sau: (ai )=(70, 80, 100); (bj )=(60,60, 80, 100) va C = (Ci)3x4 xac dinh bdi:
IO 3 9 5'
4 5 6 12J'r 6 4 7 9
a) Giai bai toan v~n tai tren.
b) Giai bai to an tren voi dieu ki<$n di€m thu thu 3 nh~n du hang.
Chti y: Sinh vU~n phdi nQP It;li di. kern vao bai thi.