đề thi tối ưu hóa

TrUong D9i hqc Kinh T€i TP.. Giai bai toan v~n tai voi s6li~u sau day.. TIm phuong an t6i u'U khac, neu co... Truong D?i hQc Kinh T eTP.. HeM HQ KhDa loTDan - Thong ke BE THI MON TOI l

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

.BE THI MON TOI lJu

Thoi gian lam bai: 75 Khong sa d\mg tai

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

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 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 ~ Xj,X2

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 eTP HeM HQ

KhDa loTDan - Thong ke

BE THI MON TOI l1u HOA (QUY HO~CH

Kh6ng sa dl,mg tili

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 4

Diu 2

[(x) = 3x] + 2x2 + 3x3 + 5x4 -7

xl +X2 + 2X 3 +2x4 ~

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)

D~3

Cau 1

nh~t (Chll~p mo hlnh, khong giai)

Cau2

f= Xl + 4X2 ~max

2xI + X2 ~ 84

XI + 2X2 ~ 42

XI + 4X2 ~ 70

XJ,X2 ~O

c6

Cau3

3 8 6J (aj) = (30, 70, 100)

«Cij» = [ 5 5 10 (bj ) =(30, 50, 80)

8 6 10

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

2Xt+x2+2x3 6 4xI +2x2 +3x3 22

Xj20,j=1,3

Ciiu 2

Cho bai toan (P):

x3 +x4 =7

Xj20,j=1,4

Ciiu 3

IO 3 9 5'\

4 5 6 12J'

r\ 6 4 7 9